[
  {
    "name": "Canonical driver",
    "description": "Synthetic canonical driver sweep; only declared fields change while the topic contract remains fixed.",
    "canonical_step": 30,
    "summary": {
      "focus_step": 30,
      "focus_kind": "canonical-fixture",
      "canonical_output_match": true,
      "state_counts": {
        "converged": 61
      },
      "value_min": 3.981454432002,
      "value_max": 6.080841995892,
      "segments": [
        {
          "start_step": 0,
          "end_step": 60,
          "state": "converged",
          "decision": "merton-equity-system-solved",
          "start_value_label": "6.0808 sigma",
          "end_value_label": "3.9815 sigma"
        }
      ]
    },
    "states": [
      {
        "step": 0,
        "value": 6.080841995892,
        "value_label": "6.0808 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 6.0808 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 25.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 144.261138337498,
          "asset_volatility": 0.291138698139,
          "distance_to_default": 6.080841995892,
          "physical_default_probability": 5.98e-10,
          "risk_neutral_default_probability": 1.131e-09,
          "iterations": 1,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 1,
        "value": 5.955950977464,
        "value_label": "5.9560 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.9560 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 26.833333333333,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 146.040288480726,
          "asset_volatility": 0.287591872451,
          "distance_to_default": 5.955950977464,
          "physical_default_probability": 1.293e-09,
          "risk_neutral_default_probability": 2.434e-09,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 2,
        "value": 5.842005332514,
        "value_label": "5.8420 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.8420 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 28.666666666667,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 147.819438622359,
          "asset_volatility": 0.284130425795,
          "distance_to_default": 5.842005332514,
          "physical_default_probability": 2.579e-09,
          "risk_neutral_default_probability": 4.835e-09,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 3,
        "value": 5.73752723459,
        "value_label": "5.7375 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.7375 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 30.5,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 149.598588761262,
          "asset_volatility": 0.280751312021,
          "distance_to_default": 5.73752723459,
          "physical_default_probability": 4.803e-09,
          "risk_neutral_default_probability": 8.975e-09,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 4,
        "value": 5.641307324268,
        "value_label": "5.6413 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.6413 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 32.333333333333,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 151.37773889576,
          "asset_volatility": 0.277451628206,
          "distance_to_default": 5.641307324268,
          "physical_default_probability": 8.438e-09,
          "risk_neutral_default_probability": 1.5724e-08,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 5,
        "value": 5.552344303681,
        "value_label": "5.5523 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.5523 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 34.166666666667,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 153.156889023508,
          "asset_volatility": 0.274228606335,
          "distance_to_default": 5.552344303681,
          "physical_default_probability": 1.4093e-08,
          "risk_neutral_default_probability": 2.6203e-08,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 6,
        "value": 5.469800515761,
        "value_label": "5.4698 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.4698 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 36.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 154.936039141359,
          "asset_volatility": 0.271079605563,
          "distance_to_default": 5.469800515761,
          "physical_default_probability": 2.2527e-08,
          "risk_neutral_default_probability": 4.1811e-08,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 7,
        "value": 5.392968701767,
        "value_label": "5.3930 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.3930 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 37.833333333333,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 156.715189245239,
          "asset_volatility": 0.268002105,
          "distance_to_default": 5.392968701767,
          "physical_default_probability": 3.4652e-08,
          "risk_neutral_default_probability": 6.423e-08,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 8,
        "value": 5.321246733774,
        "value_label": "5.3212 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.3212 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 39.666666666667,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 158.494339330046,
          "asset_volatility": 0.264993696977,
          "distance_to_default": 5.321246733774,
          "physical_default_probability": 5.1529e-08,
          "risk_neutral_default_probability": 9.5425e-08,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 9,
        "value": 5.254118139145,
        "value_label": "5.2541 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.2541 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 41.5,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 160.273489389558,
          "asset_volatility": 0.262052080767,
          "distance_to_default": 5.254118139145,
          "physical_default_probability": 7.4368e-08,
          "risk_neutral_default_probability": 1.37635e-07,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 10,
        "value": 5.191136899453,
        "value_label": "5.1911 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.1911 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 43.333333333333,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 162.052639416384,
          "asset_volatility": 0.259175056713,
          "distance_to_default": 5.191136899453,
          "physical_default_probability": 1.04507e-07,
          "risk_neutral_default_probability": 1.93356e-07,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 11,
        "value": 5.13191544984,
        "value_label": "5.1319 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.1319 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 45.166666666667,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 163.831789401919,
          "asset_volatility": 0.256360520743,
          "distance_to_default": 5.13191544984,
          "physical_default_probability": 1.43404e-07,
          "risk_neutral_default_probability": 2.65315e-07,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 12,
        "value": 5.076115106326,
        "value_label": "5.0761 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.0761 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 47.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 165.610939336347,
          "asset_volatility": 0.253606459232,
          "distance_to_default": 5.076115106326,
          "physical_default_probability": 1.92615e-07,
          "risk_neutral_default_probability": 3.5644e-07,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 13,
        "value": 5.023438357165,
        "value_label": "5.0234 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.0234 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 48.833333333333,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 167.39008920865,
          "asset_volatility": 0.250910944196,
          "distance_to_default": 5.023438357165,
          "physical_default_probability": 2.53773e-07,
          "risk_neutral_default_probability": 4.69824e-07,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 14,
        "value": 4.97362260109,
        "value_label": "4.9736 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.9736 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 50.666666666667,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 169.169239006662,
          "asset_volatility": 0.248272128784,
          "distance_to_default": 4.97362260109,
          "physical_default_probability": 3.28566e-07,
          "risk_neutral_default_probability": 6.08691e-07,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 15,
        "value": 4.926435019995,
        "value_label": "4.9264 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.9264 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 52.5,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 170.948388717124,
          "asset_volatility": 0.245688243056,
          "distance_to_default": 4.926435019995,
          "physical_default_probability": 4.18717e-07,
          "risk_neutral_default_probability": 7.76356e-07,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 16,
        "value": 4.88166834935,
        "value_label": "4.8817 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.8817 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 54.333333333333,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 172.727538325771,
          "asset_volatility": 0.243157590019,
          "distance_to_default": 4.88166834935,
          "physical_default_probability": 5.2596e-07,
          "risk_neutral_default_probability": 9.76192e-07,
          "iterations": 2,
          "residual": 1e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 17,
        "value": 4.839137365175,
        "value_label": "4.8391 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.8391 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 56.166666666667,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 174.506687817426,
          "asset_volatility": 0.240678541903,
          "distance_to_default": 4.839137365175,
          "physical_default_probability": 6.52019e-07,
          "risk_neutral_default_probability": 1.211586e-06,
          "iterations": 2,
          "residual": 1e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 18,
        "value": 4.798675947531,
        "value_label": "4.7987 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.7987 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 58.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 176.285837176112,
          "asset_volatility": 0.238249536666,
          "distance_to_default": 4.798675947531,
          "physical_default_probability": 7.9859e-07,
          "risk_neutral_default_probability": 1.485913e-06,
          "iterations": 2,
          "residual": 1e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 19,
        "value": 4.760134611283,
        "value_label": "4.7601 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.7601 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 59.833333333333,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 178.064986385166,
          "asset_volatility": 0.235869074709,
          "distance_to_default": 4.760134611283,
          "physical_default_probability": 9.67319e-07,
          "risk_neutral_default_probability": 1.802498e-06,
          "iterations": 2,
          "residual": 2e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 20,
        "value": 4.723378418258,
        "value_label": "4.7234 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.7234 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 61.666666666667,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 179.844135427362,
          "asset_volatility": 0.233535715777,
          "distance_to_default": 4.723378418258,
          "physical_default_probability": 1.159793e-06,
          "risk_neutral_default_probability": 2.164593e-06,
          "iterations": 2,
          "residual": 3e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 21,
        "value": 4.688285202668,
        "value_label": "4.6883 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.6883 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 63.5,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 181.623284285033,
          "asset_volatility": 0.23124807606,
          "distance_to_default": 4.688285202668,
          "physical_default_probability": 1.377519e-06,
          "risk_neutral_default_probability": 2.575346e-06,
          "iterations": 2,
          "residual": 4e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 22,
        "value": 4.654744055455,
        "value_label": "4.6547 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.6547 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 65.333333333333,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 183.402432940198,
          "asset_volatility": 0.229004825441,
          "distance_to_default": 4.654744055455,
          "physical_default_probability": 1.621917e-06,
          "risk_neutral_default_probability": 3.037782e-06,
          "iterations": 2,
          "residual": 6e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 23,
        "value": 4.622654023815,
        "value_label": "4.6227 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.6227 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 67.166666666667,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 185.181581374683,
          "asset_volatility": 0.226804684922,
          "distance_to_default": 4.622654023815,
          "physical_default_probability": 1.894307e-06,
          "risk_neutral_default_probability": 3.554784e-06,
          "iterations": 2,
          "residual": 8e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 24,
        "value": 4.591922990546,
        "value_label": "4.5919 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.5919 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 69.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 186.960729570234,
          "asset_volatility": 0.224646424184,
          "distance_to_default": 4.591922990546,
          "physical_default_probability": 2.195902e-06,
          "risk_neutral_default_probability": 4.129074e-06,
          "iterations": 2,
          "residual": 1.1e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 25,
        "value": 4.562466704396,
        "value_label": "4.5625 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.5625 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 70.833333333333,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 188.739877508636,
          "asset_volatility": 0.222528859293,
          "distance_to_default": 4.562466704396,
          "physical_default_probability": 2.527806e-06,
          "risk_neutral_default_probability": 4.763206e-06,
          "iterations": 2,
          "residual": 1.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 26,
        "value": 4.534207937848,
        "value_label": "4.5342 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.5342 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 72.666666666667,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 190.519025171816,
          "asset_volatility": 0.22045085053,
          "distance_to_default": 4.534207937848,
          "physical_default_probability": 2.891002e-06,
          "risk_neutral_default_probability": 5.45955e-06,
          "iterations": 2,
          "residual": 2e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 27,
        "value": 4.507075752911,
        "value_label": "4.5071 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.5071 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 74.5,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 192.298172541939,
          "asset_volatility": 0.218411300344,
          "distance_to_default": 4.507075752911,
          "physical_default_probability": 3.286359e-06,
          "risk_neutral_default_probability": 6.220291e-06,
          "iterations": 2,
          "residual": 2.6e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 28,
        "value": 4.481004858862,
        "value_label": "4.4810 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4810 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 76.333333333333,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 194.077319601499,
          "asset_volatility": 0.21640915142,
          "distance_to_default": 4.481004858862,
          "physical_default_probability": 3.714621e-06,
          "risk_neutral_default_probability": 7.04742e-06,
          "iterations": 2,
          "residual": 3.4e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 29,
        "value": 4.455935048568,
        "value_label": "4.4559 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4559 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 78.166666666667,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 195.856466333404,
          "asset_volatility": 0.214443384844,
          "distance_to_default": 4.455935048568,
          "physical_default_probability": 4.176416e-06,
          "risk_neutral_default_probability": 7.942733e-06,
          "iterations": 2,
          "residual": 4.3e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 30,
        "value": 4.431810702245,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702245,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 31,
        "value": 4.408580349267,
        "value_label": "4.4086 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4086 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 81.833333333333,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 199.414758748367,
          "asset_volatility": 0.210617104833,
          "distance_to_default": 4.408580349267,
          "physical_default_probability": 5.202521e-06,
          "risk_neutral_default_probability": 9.944121e-06,
          "iterations": 2,
          "residual": 6.9e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 32,
        "value": 4.386196280166,
        "value_label": "4.3862 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.3862 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 83.666666666667,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 201.193904399917,
          "asset_volatility": 0.208754730487,
          "distance_to_default": 4.386196280166,
          "physical_default_probability": 5.767502e-06,
          "risk_neutral_default_probability": 1.1052819e-05,
          "iterations": 2,
          "residual": 8.6e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 33,
        "value": 4.364614202112,
        "value_label": "4.3646 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.3646 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 85.5,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 202.973049660898,
          "asset_volatility": 0.206925013652,
          "distance_to_default": 4.364614202112,
          "physical_default_probability": 6.367365e-06,
          "risk_neutral_default_probability": 1.2234954e-05,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 34,
        "value": 4.343792932252,
        "value_label": "4.3438 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.3438 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 87.333333333333,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 204.752194517211,
          "asset_volatility": 0.205127103263,
          "distance_to_default": 4.343792932252,
          "physical_default_probability": 7.002176e-06,
          "risk_neutral_default_probability": 1.3491373e-05,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 35,
        "value": 4.323694124035,
        "value_label": "4.3237 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.3237 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 89.166666666667,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 206.531338955486,
          "asset_volatility": 0.203360177566,
          "distance_to_default": 4.323694124035,
          "physical_default_probability": 7.6719e-06,
          "risk_neutral_default_probability": 1.4822745e-05,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 36,
        "value": 4.304282022427,
        "value_label": "4.3043 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.3043 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 91.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 208.310482963105,
          "asset_volatility": 0.20162344286,
          "distance_to_default": 4.304282022427,
          "physical_default_probability": 8.376407e-06,
          "risk_neutral_default_probability": 1.6229571e-05,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 37,
        "value": 4.28552324446,
        "value_label": "4.2855 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.2855 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 92.833333333333,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 210.08962652823,
          "asset_volatility": 0.199916132315,
          "distance_to_default": 4.28552324446,
          "physical_default_probability": 9.115479e-06,
          "risk_neutral_default_probability": 1.7712191e-05,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 38,
        "value": 4.267386582064,
        "value_label": "4.2674 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.2674 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 94.666666666667,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 211.86876963981,
          "asset_volatility": 0.19823750484,
          "distance_to_default": 4.267386582064,
          "physical_default_probability": 9.888813e-06,
          "risk_neutral_default_probability": 1.9270789e-05,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 39,
        "value": 4.249842824556,
        "value_label": "4.2498 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.2498 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 96.5,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 213.647912287592,
          "asset_volatility": 0.196586844013,
          "distance_to_default": 4.249842824556,
          "physical_default_probability": 1.0696028e-05,
          "risk_neutral_default_probability": 2.0905402e-05,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 40,
        "value": 4.23286459851,
        "value_label": "4.2329 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.2329 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 98.333333333333,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 215.427054462126,
          "asset_volatility": 0.194963457062,
          "distance_to_default": 4.23286459851,
          "physical_default_probability": 1.1536672e-05,
          "risk_neutral_default_probability": 2.2615929e-05,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 41,
        "value": 4.216426223015,
        "value_label": "4.2164 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.2164 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 100.166666666667,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 217.206196154762,
          "asset_volatility": 0.193366673897,
          "distance_to_default": 4.216426223015,
          "physical_default_probability": 1.2410222e-05,
          "risk_neutral_default_probability": 2.4402139e-05,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 42,
        "value": 4.20050357862,
        "value_label": "4.2005 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.2005 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 102.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 218.985337357644,
          "asset_volatility": 0.191795846188,
          "distance_to_default": 4.20050357862,
          "physical_default_probability": 1.3316098e-05,
          "risk_neutral_default_probability": 2.6263677e-05,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 43,
        "value": 4.185073988441,
        "value_label": "4.1851 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.1851 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 103.833333333333,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 220.764478063706,
          "asset_volatility": 0.190250346492,
          "distance_to_default": 4.185073988441,
          "physical_default_probability": 1.4253662e-05,
          "risk_neutral_default_probability": 2.8200077e-05,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 44,
        "value": 4.170116110135,
        "value_label": "4.1701 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.1701 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 105.666666666667,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 222.543618266655,
          "asset_volatility": 0.188729567413,
          "distance_to_default": 4.170116110135,
          "physical_default_probability": 1.5222224e-05,
          "risk_neutral_default_probability": 3.0210763e-05,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 45,
        "value": 4.155609837568,
        "value_label": "4.1556 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.1556 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 107.5,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 224.322757960959,
          "asset_volatility": 0.187232920813,
          "distance_to_default": 4.155609837568,
          "physical_default_probability": 1.6221052e-05,
          "risk_neutral_default_probability": 3.2295065e-05,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 46,
        "value": 4.141536211179,
        "value_label": "4.1415 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.1415 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 109.333333333333,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 226.101897141829,
          "asset_volatility": 0.185759837049,
          "distance_to_default": 4.141536211179,
          "physical_default_probability": 1.724937e-05,
          "risk_neutral_default_probability": 3.4452219e-05,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 47,
        "value": 4.127877336137,
        "value_label": "4.1279 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.1279 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 111.166666666667,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 227.881035805204,
          "asset_volatility": 0.184309764259,
          "distance_to_default": 4.127877336137,
          "physical_default_probability": 1.8306366e-05,
          "risk_neutral_default_probability": 3.668138e-05,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 48,
        "value": 4.114616307501,
        "value_label": "4.1146 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.1146 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 113.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 229.660173947723,
          "asset_volatility": 0.182882167665,
          "distance_to_default": 4.114616307501,
          "physical_default_probability": 1.9391199e-05,
          "risk_neutral_default_probability": 3.8981626e-05,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 49,
        "value": 4.1017371417,
        "value_label": "4.1017 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.1017 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 114.833333333333,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 231.43931156671,
          "asset_volatility": 0.181476528925,
          "distance_to_default": 4.1017371417,
          "physical_default_probability": 2.0502998e-05,
          "risk_neutral_default_probability": 4.1351966e-05,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 50,
        "value": 4.089224713685,
        "value_label": "4.0892 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.0892 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 116.666666666667,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 233.218448660146,
          "asset_volatility": 0.180092345502,
          "distance_to_default": 4.089224713685,
          "physical_default_probability": 2.164087e-05,
          "risk_neutral_default_probability": 4.3791347e-05,
          "iterations": 3,
          "residual": 1e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 51,
        "value": 4.077064699238,
        "value_label": "4.0771 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.0771 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 118.5,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 234.997585226648,
          "asset_volatility": 0.178729130066,
          "distance_to_default": 4.077064699238,
          "physical_default_probability": 2.2803903e-05,
          "risk_neutral_default_probability": 4.6298659e-05,
          "iterations": 3,
          "residual": 1e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 52,
        "value": 4.06524352192,
        "value_label": "4.0652 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.0652 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 120.333333333333,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 236.776721265443,
          "asset_volatility": 0.177386409927,
          "distance_to_default": 4.06524352192,
          "physical_default_probability": 2.3991167e-05,
          "risk_neutral_default_probability": 4.8872743e-05,
          "iterations": 3,
          "residual": 1e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 53,
        "value": 4.053748304234,
        "value_label": "4.0537 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.0537 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 122.166666666667,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 238.55585677634,
          "asset_volatility": 0.176063726485,
          "distance_to_default": 4.053748304234,
          "physical_default_probability": 2.5201723e-05,
          "risk_neutral_default_probability": 5.1512394e-05,
          "iterations": 3,
          "residual": 1e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 54,
        "value": 4.042566822621,
        "value_label": "4.0426 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.0426 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 124.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 240.33499175971,
          "asset_volatility": 0.174760634713,
          "distance_to_default": 4.042566822621,
          "physical_default_probability": 2.6434619e-05,
          "risk_neutral_default_probability": 5.4216368e-05,
          "iterations": 3,
          "residual": 1e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 55,
        "value": 4.03168746592,
        "value_label": "4.0317 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.0317 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 125.833333333333,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 242.114126216458,
          "asset_volatility": 0.173476702655,
          "distance_to_default": 4.03168746592,
          "physical_default_probability": 2.7688899e-05,
          "risk_neutral_default_probability": 5.6983388e-05,
          "iterations": 3,
          "residual": 1e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 56,
        "value": 4.021099197,
        "value_label": "4.0211 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.0211 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 127.666666666667,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 243.893260147992,
          "asset_volatility": 0.172211510953,
          "distance_to_default": 4.021099197,
          "physical_default_probability": 2.8963602e-05,
          "risk_neutral_default_probability": 5.9812148e-05,
          "iterations": 3,
          "residual": 1e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 57,
        "value": 4.010791517269,
        "value_label": "4.0108 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.0108 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 129.5,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 245.672393556208,
          "asset_volatility": 0.170964652389,
          "distance_to_default": 4.010791517269,
          "physical_default_probability": 3.0257765e-05,
          "risk_neutral_default_probability": 6.2701314e-05,
          "iterations": 3,
          "residual": 2e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 58,
        "value": 4.000754433818,
        "value_label": "4.0008 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.0008 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 131.333333333333,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 247.451526443455,
          "asset_volatility": 0.169735731451,
          "distance_to_default": 4.000754433818,
          "physical_default_probability": 3.1570428e-05,
          "risk_neutral_default_probability": 6.5649535e-05,
          "iterations": 3,
          "residual": 2e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 59,
        "value": 3.990978428966,
        "value_label": "3.9910 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.9910 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 133.166666666667,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 249.230658812515,
          "asset_volatility": 0.168524363914,
          "distance_to_default": 3.990978428966,
          "physical_default_probability": 3.2900633e-05,
          "risk_neutral_default_probability": 6.8655442e-05,
          "iterations": 3,
          "residual": 2e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 60,
        "value": 3.981454432002,
        "value_label": "3.9815 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.9815 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 135.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 251.009790666578,
          "asset_volatility": 0.167330176441,
          "distance_to_default": 3.981454432002,
          "physical_default_probability": 3.4247427e-05,
          "risk_neutral_default_probability": 7.1717651e-05,
          "iterations": 3,
          "residual": 3e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      }
    ]
  },
  {
    "name": "Adverse shift",
    "description": "Synthetic adverse shift sweep; only declared fields change while the topic contract remains fixed.",
    "canonical_step": 30,
    "summary": {
      "focus_step": 30,
      "focus_kind": "comparison",
      "canonical_output_match": false,
      "state_counts": {
        "converged": 61
      },
      "value_min": 1.16577117396,
      "value_max": 13.199647087344,
      "segments": [
        {
          "start_step": 0,
          "end_step": 60,
          "state": "converged",
          "decision": "merton-equity-system-solved",
          "start_value_label": "13.1996 sigma",
          "end_value_label": "1.1658 sigma"
        }
      ]
    },
    "states": [
      {
        "step": 0,
        "value": 13.199647087344,
        "value_label": "13.1996 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 13.1996 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.12,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635642683881,
          "asset_volatility": 0.072861351346,
          "distance_to_default": 13.199647087344,
          "physical_default_probability": 0.0,
          "risk_neutral_default_probability": 0.0,
          "iterations": 1,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 1,
        "value": 11.753641425511,
        "value_label": "11.7536 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 11.7536 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.134666666667,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635642683881,
          "asset_volatility": 0.081766627621,
          "distance_to_default": 11.753641425511,
          "physical_default_probability": 0.0,
          "risk_neutral_default_probability": 0.0,
          "iterations": 1,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 2,
        "value": 10.590797964762,
        "value_label": "10.5908 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 10.5908 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.149333333333,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635642683881,
          "asset_volatility": 0.090671903897,
          "distance_to_default": 10.590797964762,
          "physical_default_probability": 0.0,
          "risk_neutral_default_probability": 0.0,
          "iterations": 1,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 3,
        "value": 9.635146358463,
        "value_label": "9.6351 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 9.6351 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.164,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635642683881,
          "asset_volatility": 0.099577180172,
          "distance_to_default": 9.635146358463,
          "physical_default_probability": 0.0,
          "risk_neutral_default_probability": 0.0,
          "iterations": 1,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 4,
        "value": 8.835661746937,
        "value_label": "8.8357 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 8.8357 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.178666666667,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635642683881,
          "asset_volatility": 0.108482456448,
          "distance_to_default": 8.835661746937,
          "physical_default_probability": 0.0,
          "risk_neutral_default_probability": 0.0,
          "iterations": 1,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 5,
        "value": 8.1568026762,
        "value_label": "8.1568 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 8.1568 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.193333333333,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635642683881,
          "asset_volatility": 0.117387732723,
          "distance_to_default": 8.1568026762,
          "physical_default_probability": 0.0,
          "risk_neutral_default_probability": 0.0,
          "iterations": 1,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 6,
        "value": 7.573052204933,
        "value_label": "7.5731 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 7.5731 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.208,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.63564268388,
          "asset_volatility": 0.126293008999,
          "distance_to_default": 7.573052204933,
          "physical_default_probability": 0.0,
          "risk_neutral_default_probability": 0.0,
          "iterations": 1,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 7,
        "value": 7.065616418259,
        "value_label": "7.0656 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 7.0656 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.222666666667,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635642683875,
          "asset_volatility": 0.135198285275,
          "distance_to_default": 7.065616418259,
          "physical_default_probability": 1e-12,
          "risk_neutral_default_probability": 4e-12,
          "iterations": 1,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 8,
        "value": 6.620347087971,
        "value_label": "6.6203 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 6.6203 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.237333333333,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635642683763,
          "asset_volatility": 0.144103561554,
          "distance_to_default": 6.620347087971,
          "physical_default_probability": 1.8e-11,
          "risk_neutral_default_probability": 7.2e-11,
          "iterations": 1,
          "residual": 4e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 9,
        "value": 6.226389751852,
        "value_label": "6.2264 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 6.2264 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.252,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635642682383,
          "asset_volatility": 0.153008837875,
          "distance_to_default": 6.226389751852,
          "physical_default_probability": 2.39e-10,
          "risk_neutral_default_probability": 8.18e-10,
          "iterations": 1,
          "residual": 4.9e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 10,
        "value": 5.875277920838,
        "value_label": "5.8753 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.8753 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.266666666667,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635642670944,
          "asset_volatility": 0.161914114505,
          "distance_to_default": 5.875277920838,
          "physical_default_probability": 2.111e-09,
          "risk_neutral_default_probability": 6.352e-09,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 11,
        "value": 5.560310593553,
        "value_label": "5.5603 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.5603 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.281333333333,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635642602197,
          "asset_volatility": 0.170819392812,
          "distance_to_default": 5.560310593553,
          "physical_default_probability": 1.3465e-08,
          "risk_neutral_default_probability": 3.6286e-08,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 12,
        "value": 5.276114780199,
        "value_label": "5.2761 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.2761 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.296,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635642283618,
          "asset_volatility": 0.179724678073,
          "distance_to_default": 5.276114780199,
          "physical_default_probability": 6.5976e-08,
          "risk_neutral_default_probability": 1.61769e-07,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 13,
        "value": 5.018331843934,
        "value_label": "5.0183 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.0183 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.310666666667,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635641090185,
          "asset_volatility": 0.188629986574,
          "distance_to_default": 5.018331843934,
          "physical_default_probability": 2.6061e-07,
          "risk_neutral_default_probability": 5.89036e-07,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 14,
        "value": 4.783388532893,
        "value_label": "4.7834 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.7834 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.325333333333,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635637339238,
          "asset_volatility": 0.197535360039,
          "distance_to_default": 4.783388532893,
          "physical_default_probability": 8.61822e-07,
          "risk_neutral_default_probability": 1.814981e-06,
          "iterations": 2,
          "residual": 2e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 15,
        "value": 4.568327100707,
        "value_label": "4.5683 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.5683 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.34,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.63562715204,
          "asset_volatility": 0.206440890152,
          "distance_to_default": 4.568327100707,
          "physical_default_probability": 2.458162e-06,
          "risk_neutral_default_probability": 4.866828e-06,
          "iterations": 2,
          "residual": 1.7e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 16,
        "value": 4.370677427292,
        "value_label": "4.3707 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.3707 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.354666666667,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635602672634,
          "asset_volatility": 0.215346754197,
          "distance_to_default": 4.370677427292,
          "physical_default_probability": 6.193083e-06,
          "risk_neutral_default_probability": 1.1613755e-05,
          "iterations": 2,
          "residual": 9.3e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 17,
        "value": 4.188359528546,
        "value_label": "4.1884 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.1884 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.369333333333,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635549623971,
          "asset_volatility": 0.224253260187,
          "distance_to_default": 4.188359528546,
          "physical_default_probability": 1.4048907e-05,
          "risk_neutral_default_probability": 2.5111993e-05,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 18,
        "value": 4.019608423798,
        "value_label": "4.0196 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.0196 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.384,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.63544432184,
          "asset_volatility": 0.233160897241,
          "distance_to_default": 4.019608423798,
          "physical_default_probability": 2.9147475e-05,
          "risk_neutral_default_probability": 4.992792e-05,
          "iterations": 3,
          "residual": 1e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 19,
        "value": 3.862915699472,
        "value_label": "3.8629 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.8629 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.398666666667,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635250392026,
          "asset_volatility": 0.242070385283,
          "distance_to_default": 3.862915699472,
          "physical_default_probability": 5.602084e-05,
          "risk_neutral_default_probability": 9.2382448e-05,
          "iterations": 3,
          "residual": 3e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 20,
        "value": 3.716983695984,
        "value_label": "3.7170 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.7170 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.413333333333,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.634915507661,
          "asset_volatility": 0.250982717949,
          "distance_to_default": 3.716983695984,
          "physical_default_probability": 0.000100807724,
          "risk_neutral_default_probability": 0.000160673928,
          "iterations": 3,
          "residual": 1.6e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 21,
        "value": 3.580689328594,
        "value_label": "3.5807 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.5807 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.428,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.634368466799,
          "asset_volatility": 0.259899193744,
          "distance_to_default": 3.580689328594,
          "physical_default_probability": 0.000171344462,
          "risk_neutral_default_probability": 0.000264859586,
          "iterations": 3,
          "residual": 6.4e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 22,
        "value": 3.453055309986,
        "value_label": "3.4531 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.4531 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.442666666667,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.633516873478,
          "asset_volatility": 0.268821432458,
          "distance_to_default": 3.453055309986,
          "physical_default_probability": 0.000277137671,
          "risk_neutral_default_probability": 0.000416699524,
          "iterations": 4,
          "residual": 1e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 23,
        "value": 3.33322708659,
        "value_label": "3.3332 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.3332 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.457333333333,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.632245592137,
          "asset_volatility": 0.277751376074,
          "distance_to_default": 3.33322708659,
          "physical_default_probability": 0.000429224224,
          "risk_neutral_default_probability": 0.000629386483,
          "iterations": 4,
          "residual": 2e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 24,
        "value": 3.220454202549,
        "value_label": "3.2205 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.2205 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.472,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.630416041496,
          "asset_volatility": 0.286691275325,
          "distance_to_default": 3.220454202549,
          "physical_default_probability": 0.000639938202,
          "risk_neutral_default_probability": 0.000917195831,
          "iterations": 4,
          "residual": 9e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 25,
        "value": 3.114075108787,
        "value_label": "3.1141 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.1141 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.486666666667,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.627866302035,
          "asset_volatility": 0.295643664389,
          "distance_to_default": 3.114075108787,
          "physical_default_probability": 0.000922612554,
          "risk_neutral_default_probability": 0.001295093578,
          "iterations": 4,
          "residual": 3.2e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 26,
        "value": 3.013504666377,
        "value_label": "3.0135 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.0135 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.501333333333,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.624411942569,
          "asset_volatility": 0.304611326884,
          "distance_to_default": 3.013504666377,
          "physical_default_probability": 0.001291245348,
          "risk_neutral_default_probability": 0.001778337259,
          "iterations": 5,
          "residual": 1e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 27,
        "value": 2.918223771282,
        "value_label": "2.9182 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 2.9182 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.516,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.619847431068,
          "asset_volatility": 0.313597256466,
          "distance_to_default": 2.918223771282,
          "physical_default_probability": 0.001760158108,
          "risk_neutral_default_probability": 0.00238209778,
          "iterations": 5,
          "residual": 3e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 28,
        "value": 2.827770663341,
        "value_label": "2.8278 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 2.8278 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.530666666667,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.613947978927,
          "asset_volatility": 0.322604615039,
          "distance_to_default": 2.827770663341,
          "physical_default_probability": 0.002343668633,
          "risk_neutral_default_probability": 0.003121122037,
          "iterations": 5,
          "residual": 9e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 29,
        "value": 2.741733585824,
        "value_label": "2.7417 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 2.7417 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.545333333333,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.606471672332,
          "asset_volatility": 0.331636691022,
          "distance_to_default": 2.741733585824,
          "physical_default_probability": 0.003055794449,
          "risk_neutral_default_probability": 0.004009448043,
          "iterations": 5,
          "residual": 2.8e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 30,
        "value": 2.659744539577,
        "value_label": "2.6597 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 2.6597 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.56,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.597161760249,
          "asset_volatility": 0.340696859578,
          "distance_to_default": 2.659744539577,
          "physical_default_probability": 0.003909996957,
          "risk_neutral_default_probability": 0.005060177383,
          "iterations": 5,
          "residual": 7.7e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 31,
        "value": 2.581473934209,
        "value_label": "2.5815 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 2.5815 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.574666666667,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.585748991407,
          "asset_volatility": 0.349788546038,
          "distance_to_default": 2.581473934209,
          "physical_default_probability": 0.004918971015,
          "risk_neutral_default_probability": 0.00628530459,
          "iterations": 6,
          "residual": 4e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 32,
        "value": 2.506625982542,
        "value_label": "2.5066 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 2.5066 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.589333333333,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.571953918583,
          "asset_volatility": 0.358915193269,
          "distance_to_default": 2.506625982542,
          "physical_default_probability": 0.006094480608,
          "risk_neutral_default_probability": 0.00769559946,
          "iterations": 6,
          "residual": 1.2e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 33,
        "value": 2.43493471655,
        "value_label": "2.4349 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 2.4349 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.604,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.555489108427,
          "asset_volatility": 0.368080233338,
          "distance_to_default": 2.43493471655,
          "physical_default_probability": 0.007447238336,
          "risk_neutral_default_probability": 0.009300536189,
          "iterations": 6,
          "residual": 3.2e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 34,
        "value": 2.366160528208,
        "value_label": "2.3662 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 2.3662 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.618666666667,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.5360612202,
          "asset_volatility": 0.377287063448,
          "distance_to_default": 2.366160528208,
          "physical_default_probability": 0.008986824598,
          "risk_neutral_default_probability": 0.011108262249,
          "iterations": 6,
          "residual": 7.7e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 35,
        "value": 2.300087156377,
        "value_label": "2.3001 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 2.3001 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.633333333333,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.513372928632,
          "asset_volatility": 0.386539025983,
          "distance_to_default": 2.300087156377,
          "physical_default_probability": 0.010721641387,
          "risk_neutral_default_probability": 0.013125599741,
          "iterations": 7,
          "residual": 7e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 36,
        "value": 2.236519055648,
        "value_label": "2.2365 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 2.2365 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.648,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.487124683677,
          "asset_volatility": 0.395839392286,
          "distance_to_default": 2.236519055648,
          "physical_default_probability": 0.012658895251,
          "risk_neutral_default_probability": 0.01535807237,
          "iterations": 7,
          "residual": 1.7e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 37,
        "value": 2.175279093106,
        "value_label": "2.1753 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 2.1753 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.662666666667,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.457016302091,
          "asset_volatility": 0.405191349839,
          "distance_to_default": 2.175279093106,
          "physical_default_probability": 0.014804604128,
          "risk_neutral_default_probability": 0.017809951859,
          "iterations": 7,
          "residual": 3.9e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 38,
        "value": 2.116206528775,
        "value_label": "2.1162 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 2.1162 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.677333333333,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.42274840155,
          "asset_volatility": 0.414597992333,
          "distance_to_default": 2.116206528775,
          "physical_default_probability": 0.017163623098,
          "risk_neutral_default_probability": 0.02048431844,
          "iterations": 7,
          "residual": 8.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 39,
        "value": 2.059155241332,
        "value_label": "2.0592 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 2.0592 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.692,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.384023683108,
          "asset_volatility": 0.424062312279,
          "distance_to_default": 2.059155241332,
          "physical_default_probability": 0.019739684664,
          "risk_neutral_default_probability": 0.023383130967,
          "iterations": 8,
          "residual": 1.1e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 40,
        "value": 2.003992167275,
        "value_label": "2.0040 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 2.0040 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.706666666667,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.340548078942,
          "asset_volatility": 0.433587195673,
          "distance_to_default": 2.003992167275,
          "physical_default_probability": 0.022535449738,
          "risk_neutral_default_probability": 0.026507302956,
          "iterations": 8,
          "residual": 2.4e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 41,
        "value": 1.950595925101,
        "value_label": "1.9506 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 1.9506 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.721333333333,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.292031770499,
          "asset_volatility": 0.443175418485,
          "distance_to_default": 1.950595925101,
          "physical_default_probability": 0.025552566169,
          "risk_neutral_default_probability": 0.029856781707,
          "iterations": 8,
          "residual": 5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 42,
        "value": 1.89885560158,
        "value_label": "1.8989 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 1.8989 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.736,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.238190099294,
          "asset_volatility": 0.452829644507,
          "distance_to_default": 1.89885560158,
          "physical_default_probability": 0.02879173213,
          "risk_neutral_default_probability": 0.033430628189,
          "iterations": 8,
          "residual": 1e-10,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 43,
        "value": 1.848669678926,
        "value_label": "1.8487 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 1.8487 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.750666666667,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.178744375737,
          "asset_volatility": 0.462552424392,
          "distance_to_default": 1.848669678926,
          "physical_default_probability": 0.032252762257,
          "risk_neutral_default_probability": 0.037227096035,
          "iterations": 9,
          "residual": 1.6e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 44,
        "value": 1.799945085794,
        "value_label": "1.7999 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 1.7999 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.765333333333,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.113422606053,
          "asset_volatility": 0.47234619553,
          "distance_to_default": 1.799945085794,
          "physical_default_probability": 0.035934654812,
          "risk_neutral_default_probability": 0.041243708349,
          "iterations": 9,
          "residual": 3.3e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 45,
        "value": 1.752596355635,
        "value_label": "1.7526 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 1.7526 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.78,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.041960134368,
          "asset_volatility": 0.482213282738,
          "distance_to_default": 1.752596355635,
          "physical_default_probability": 0.039835658643,
          "risk_neutral_default_probability": 0.045477331521,
          "iterations": 9,
          "residual": 6.3e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 46,
        "value": 1.706544880259,
        "value_label": "1.7065 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 1.7065 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.794666666667,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 196.964100224078,
          "asset_volatility": 0.492155899411,
          "distance_to_default": 1.706544880259,
          "physical_default_probability": 0.043953338842,
          "risk_neutral_default_probability": 0.04992424537,
          "iterations": 10,
          "residual": 1.2e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 47,
        "value": 1.661718246473,
        "value_label": "1.6617 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 1.6617 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.809333333333,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 196.879594581142,
          "asset_volatility": 0.502176149065,
          "distance_to_default": 1.661718246473,
          "physical_default_probability": 0.048284640428,
          "risk_neutral_default_probability": 0.054580209301,
          "iterations": 10,
          "residual": 2.4e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 48,
        "value": 1.618049645272,
        "value_label": "1.6180 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 1.6180 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.824,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 196.788203819629,
          "asset_volatility": 0.512276027244,
          "distance_to_default": 1.618049645272,
          "physical_default_probability": 0.05282594955,
          "risk_neutral_default_probability": 0.059440524314,
          "iterations": 10,
          "residual": 4.4e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 49,
        "value": 1.575477345647,
        "value_label": "1.5755 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 1.5755 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.838666666667,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 196.689697887607,
          "asset_volatility": 0.522457423562,
          "distance_to_default": 1.575477345647,
          "physical_default_probability": 0.057573151792,
          "risk_neutral_default_probability": 0.06450009075,
          "iterations": 10,
          "residual": 7.9e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 50,
        "value": 1.533944224639,
        "value_label": "1.5339 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 1.5339 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.853333333333,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 196.583856448508,
          "asset_volatility": 0.532722123918,
          "distance_to_default": 1.533944224639,
          "physical_default_probability": 0.062521687427,
          "risk_neutral_default_probability": 0.069753461868,
          "iterations": 11,
          "residual": 1.8e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 51,
        "value": 1.493397347622,
        "value_label": "1.4934 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 1.4934 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.868,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 196.470469232892,
          "asset_volatility": 0.543071812705,
          "distance_to_default": 1.493397347622,
          "physical_default_probability": 0.067666603427,
          "risk_neutral_default_probability": 0.07519489329,
          "iterations": 11,
          "residual": 3.2e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 52,
        "value": 1.453787591968,
        "value_label": "1.4538 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 1.4538 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.882666666667,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 196.349336346796,
          "asset_volatility": 0.553508075179,
          "distance_to_default": 1.453787591968,
          "physical_default_probability": 0.073002602304,
          "risk_neutral_default_probability": 0.080818388607,
          "iterations": 11,
          "residual": 5.6e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 53,
        "value": 1.415069310157,
        "value_label": "1.4151 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 1.4151 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.897333333333,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 196.220268559713,
          "asset_volatility": 0.564032399711,
          "distance_to_default": 1.415069310157,
          "physical_default_probability": 0.078524087682,
          "risk_neutral_default_probability": 0.086617741174,
          "iterations": 11,
          "residual": 9.4e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 54,
        "value": 1.377200026965,
        "value_label": "1.3772 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 1.3772 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.912,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 196.083087558574,
          "asset_volatility": 0.574646180081,
          "distance_to_default": 1.377200026965,
          "physical_default_probability": 0.084225206758,
          "risk_neutral_default_probability": 0.092586572421,
          "iterations": 12,
          "residual": 2.4e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 55,
        "value": 1.340140167653,
        "value_label": "1.3401 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 1.3401 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.926666666667,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 195.937626185525,
          "asset_volatility": 0.585350717623,
          "distance_to_default": 1.340140167653,
          "physical_default_probability": 0.090099889644,
          "risk_neutral_default_probability": 0.098718366778,
          "iterations": 12,
          "residual": 4.1e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 56,
        "value": 1.303852812443,
        "value_label": "1.3039 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 1.3039 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.941333333333,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 195.783728635448,
          "asset_volatility": 0.596147223485,
          "distance_to_default": 1.303852812443,
          "physical_default_probability": 0.096141885897,
          "risk_neutral_default_probability": 0.105006503629,
          "iterations": 12,
          "residual": 6.7e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 57,
        "value": 1.26830347571,
        "value_label": "1.2683 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 1.2683 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.956,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 195.621250642535,
          "asset_volatility": 0.607036820685,
          "distance_to_default": 1.26830347571,
          "physical_default_probability": 0.102344798165,
          "risk_neutral_default_probability": 0.111444286287,
          "iterations": 13,
          "residual": 1.9e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 58,
        "value": 1.23345990658,
        "value_label": "1.2335 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 1.2335 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.970666666667,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 195.450059644863,
          "asset_volatility": 0.618020546086,
          "distance_to_default": 1.23345990658,
          "physical_default_probability": 0.108702113158,
          "risk_neutral_default_probability": 0.118024968282,
          "iterations": 13,
          "residual": 3.1e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 59,
        "value": 1.199291908098,
        "value_label": "1.1993 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 1.1993 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.985333333333,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 195.270034915088,
          "asset_volatility": 0.629099352435,
          "distance_to_default": 1.199291908098,
          "physical_default_probability": 0.115207230218,
          "risk_neutral_default_probability": 0.124741777283,
          "iterations": 13,
          "residual": 5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 60,
        "value": 1.16577117396,
        "value_label": "1.1658 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 1.1658 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 1.0,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 195.081067680922,
          "asset_volatility": 0.640274110197,
          "distance_to_default": 1.16577117396,
          "physical_default_probability": 0.121853487424,
          "risk_neutral_default_probability": 0.131587936634,
          "iterations": 13,
          "residual": 7.7e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      }
    ]
  },
  {
    "name": "Protective shift",
    "description": "Synthetic protective shift sweep; only declared fields change while the topic contract remains fixed.",
    "canonical_step": 30,
    "summary": {
      "focus_step": 30,
      "focus_kind": "comparison",
      "canonical_output_match": false,
      "state_counts": {
        "converged": 61
      },
      "value_min": 3.606633704308,
      "value_max": 5.308713808777,
      "segments": [
        {
          "start_step": 0,
          "end_step": 60,
          "state": "converged",
          "decision": "merton-equity-system-solved",
          "start_value_label": "3.6066 sigma",
          "end_value_label": "5.3087 sigma"
        }
      ]
    },
    "states": [
      {
        "step": 0,
        "value": 3.606633704308,
        "value_label": "3.6066 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.6066 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 30.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 107.634698574032,
          "asset_volatility": 0.097585451479,
          "distance_to_default": 3.606633704308,
          "physical_default_probability": 0.000155097529,
          "risk_neutral_default_probability": 0.000484785314,
          "iterations": 4,
          "residual": 3e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 1,
        "value": 3.630643656991,
        "value_label": "3.6306 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.6306 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 33.5,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 111.134791388425,
          "asset_volatility": 0.105531887275,
          "distance_to_default": 3.630643656991,
          "physical_default_probability": 0.000141357646,
          "risk_neutral_default_probability": 0.000409386212,
          "iterations": 4,
          "residual": 2e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 2,
        "value": 3.658115250878,
        "value_label": "3.6581 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.6581 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 37.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 114.634881393055,
          "asset_volatility": 0.112993098879,
          "distance_to_default": 3.658115250878,
          "physical_default_probability": 0.000127038399,
          "risk_neutral_default_probability": 0.000346147726,
          "iterations": 4,
          "residual": 1e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 3,
        "value": 3.687952302098,
        "value_label": "3.6880 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.6880 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 40.5,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 118.134966219194,
          "asset_volatility": 0.120012300932,
          "distance_to_default": 3.687952302098,
          "physical_default_probability": 0.000113033007,
          "risk_neutral_default_probability": 0.000293037736,
          "iterations": 4,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 4,
        "value": 3.719416838982,
        "value_label": "3.7194 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.7194 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 44.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 121.635044595657,
          "asset_volatility": 0.126627700562,
          "distance_to_default": 3.719416838982,
          "physical_default_probability": 9.9841639e-05,
          "risk_neutral_default_probability": 0.000248375892,
          "iterations": 4,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 5,
        "value": 3.751996437374,
        "value_label": "3.7520 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.7520 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 47.5,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 125.13511597913,
          "asset_volatility": 0.132873207727,
          "distance_to_default": 3.751996437374,
          "physical_default_probability": 8.7715979e-05,
          "risk_neutral_default_probability": 0.000210770481,
          "iterations": 3,
          "residual": 6.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 6,
        "value": 3.785326258721,
        "value_label": "3.7853 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.7853 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 51.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 128.635180298312,
          "asset_volatility": 0.138779026806,
          "distance_to_default": 3.785326258721,
          "physical_default_probability": 7.6753526e-05,
          "risk_neutral_default_probability": 0.000179067069,
          "iterations": 3,
          "residual": 4e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 7,
        "value": 3.819141188028,
        "value_label": "3.8191 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.8191 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 54.5,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 132.135237777766,
          "asset_volatility": 0.144372152206,
          "distance_to_default": 3.819141188028,
          "physical_default_probability": 6.695855e-05,
          "risk_neutral_default_probability": 0.00015230663,
          "iterations": 3,
          "residual": 2.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 8,
        "value": 3.85324534818,
        "value_label": "3.8532 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.8532 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 58.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 135.635288817452,
          "asset_volatility": 0.149676785868,
          "distance_to_default": 3.85324534818,
          "physical_default_probability": 5.8281243e-05,
          "risk_neutral_default_probability": 0.00012969133,
          "iterations": 3,
          "residual": 1.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 9,
        "value": 3.887492061734,
        "value_label": "3.8875 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.8875 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 61.5,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 139.135333911319,
          "asset_volatility": 0.15471469079,
          "distance_to_default": 3.887492061734,
          "physical_default_probability": 5.064265e-05,
          "risk_neutral_default_probability": 0.000110556514,
          "iterations": 3,
          "residual": 9e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 10,
        "value": 3.921770317183,
        "value_label": "3.9218 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.9218 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 65.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 142.635373593101,
          "asset_volatility": 0.15950549182,
          "distance_to_default": 3.921770317183,
          "physical_default_probability": 4.3950381e-05,
          "risk_neutral_default_probability": 9.434773e-05,
          "iterations": 3,
          "residual": 6e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 11,
        "value": 3.955995409343,
        "value_label": "3.9560 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.9560 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 68.5,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 146.135408401077,
          "asset_volatility": 0.164066932755,
          "distance_to_default": 3.955995409343,
          "physical_default_probability": 3.8108312e-05,
          "risk_neutral_default_probability": 8.0601847e-05,
          "iterations": 3,
          "residual": 4e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 12,
        "value": 3.99010233043,
        "value_label": "3.9901 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.9901 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 72.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 149.635438855923,
          "asset_volatility": 0.168415097022,
          "distance_to_default": 3.99010233043,
          "physical_default_probability": 3.3022397e-05,
          "risk_neutral_default_probability": 6.8931518e-05,
          "iterations": 3,
          "residual": 2e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 13,
        "value": 4.024041016792,
        "value_label": "4.0240 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.0240 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 75.5,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 153.135465447574,
          "asset_volatility": 0.172564597864,
          "distance_to_default": 4.024041016792,
          "physical_default_probability": 2.8603973e-05,
          "risk_neutral_default_probability": 5.9012374e-05,
          "iterations": 3,
          "residual": 1e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 14,
        "value": 4.057772873869,
        "value_label": "4.0578 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.0578 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 79.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 156.635488628174,
          "asset_volatility": 0.176528742869,
          "distance_to_default": 4.057772873869,
          "physical_default_probability": 2.4771457e-05,
          "risk_neutral_default_probability": 5.0572446e-05,
          "iterations": 3,
          "residual": 1e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 15,
        "value": 4.091268198217,
        "value_label": "4.0913 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.0913 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 82.5,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 160.135508809113,
          "asset_volatility": 0.180319676811,
          "distance_to_default": 4.091268198217,
          "physical_default_probability": 2.1451032e-05,
          "risk_neutral_default_probability": 4.3383427e-05,
          "iterations": 3,
          "residual": 1e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 16,
        "value": 4.124504239766,
        "value_label": "4.1245 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.1245 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 86.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 163.635526360713,
          "asset_volatility": 0.18394850609,
          "distance_to_default": 4.124504239766,
          "physical_default_probability": 1.8576707e-05,
          "risk_neutral_default_probability": 3.7253434e-05,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 17,
        "value": 4.157463727991,
        "value_label": "4.1575 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.1575 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 89.5,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 167.135541613591,
          "asset_volatility": 0.187425407479,
          "distance_to_default": 4.157463727991,
          "physical_default_probability": 1.6090017e-05,
          "risk_neutral_default_probability": 3.2021009e-05,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 18,
        "value": 4.190133738926,
        "value_label": "4.1901 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.1901 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 93.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 170.635554861011,
          "asset_volatility": 0.19075972346,
          "distance_to_default": 4.190133738926,
          "physical_default_probability": 1.3939504e-05,
          "risk_neutral_default_probability": 2.7550136e-05,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 19,
        "value": 4.222504815736,
        "value_label": "4.2225 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.2225 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 96.5,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 174.135566361779,
          "asset_volatility": 0.193960046043,
          "distance_to_default": 4.222504815736,
          "physical_default_probability": 1.2080112e-05,
          "risk_neutral_default_probability": 2.3726104e-05,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 20,
        "value": 4.254570280122,
        "value_label": "4.2546 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.2546 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 100.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 177.63557634335,
          "asset_volatility": 0.197034290664,
          "distance_to_default": 4.254570280122,
          "physical_default_probability": 1.0472543e-05,
          "risk_neutral_default_probability": 2.0452063e-05,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 21,
        "value": 4.286325688853,
        "value_label": "4.2863 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.2863 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 103.5,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 181.135585004974,
          "asset_volatility": 0.199989761503,
          "distance_to_default": 4.286325688853,
          "physical_default_probability": 9.082631e-06,
          "risk_neutral_default_probability": 1.7646151e-05,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 22,
        "value": 4.317768401751,
        "value_label": "4.3178 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.3178 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 107.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 184.635592520721,
          "asset_volatility": 0.202833209379,
          "distance_to_default": 4.317768401751,
          "physical_default_probability": 7.880734e-06,
          "risk_neutral_default_probability": 1.5239098e-05,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 23,
        "value": 4.348897236017,
        "value_label": "4.3489 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.3489 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 110.5,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 188.13559904234,
          "asset_volatility": 0.205570883179,
          "distance_to_default": 4.348897236017,
          "physical_default_probability": 6.84119e-06,
          "risk_neutral_default_probability": 1.3172231e-05,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 24,
        "value": 4.379712188027,
        "value_label": "4.3797 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.3797 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 114.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 191.635604701887,
          "asset_volatility": 0.208208575646,
          "distance_to_default": 4.379712188027,
          "physical_default_probability": 5.941808e-06,
          "risk_neutral_default_probability": 1.1395798e-05,
          "iterations": 2,
          "residual": 9.2e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 25,
        "value": 4.410214208218,
        "value_label": "4.4102 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4102 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 117.5,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 195.135609614122,
          "asset_volatility": 0.210751664257,
          "distance_to_default": 4.410214208218,
          "physical_default_probability": 5.163421e-06,
          "risk_neutral_default_probability": 9.867565e-06,
          "iterations": 2,
          "residual": 6.8e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 26,
        "value": 4.440405018072,
        "value_label": "4.4404 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4404 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 121.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 198.635613878662,
          "asset_volatility": 0.213205147764,
          "distance_to_default": 4.440405018072,
          "physical_default_probability": 4.489486e-06,
          "risk_neutral_default_probability": 8.551648e-06,
          "iterations": 2,
          "residual": 5.1e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 27,
        "value": 4.470286960677,
        "value_label": "4.4703 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4703 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 124.5,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 202.135617581902,
          "asset_volatility": 0.215573678954,
          "distance_to_default": 4.470286960677,
          "physical_default_probability": 3.905736e-06,
          "risk_neutral_default_probability": 7.417525e-06,
          "iterations": 2,
          "residual": 3.8e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 28,
        "value": 4.49986287825,
        "value_label": "4.4999 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4999 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 128.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 205.63562079872,
          "asset_volatility": 0.217861594065,
          "distance_to_default": 4.49986287825,
          "physical_default_probability": 3.399866e-06,
          "risk_neutral_default_probability": 6.439209e-06,
          "iterations": 2,
          "residual": 2.8e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 29,
        "value": 4.529136011418,
        "value_label": "4.5291 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.5291 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 131.5,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 209.135623593978,
          "asset_volatility": 0.220072939242,
          "distance_to_default": 4.529136011418,
          "physical_default_probability": 2.961268e-06,
          "risk_neutral_default_probability": 5.594551e-06,
          "iterations": 2,
          "residual": 2.1e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 30,
        "value": 4.558109916154,
        "value_label": "4.5581 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.5581 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 135.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 212.635626023841,
          "asset_volatility": 0.222211494397,
          "distance_to_default": 4.558109916154,
          "physical_default_probability": 2.580801e-06,
          "risk_neutral_default_probability": 4.864657e-06,
          "iterations": 2,
          "residual": 1.6e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 31,
        "value": 4.586788395104,
        "value_label": "4.5868 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.5868 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 138.5,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 216.135628136932,
          "asset_volatility": 0.224280794739,
          "distance_to_default": 4.586788395104,
          "physical_default_probability": 2.250582e-06,
          "risk_neutral_default_probability": 4.233395e-06,
          "iterations": 2,
          "residual": 1.2e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 32,
        "value": 4.615175440698,
        "value_label": "4.6152 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.6152 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 142.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 219.635629975337,
          "asset_volatility": 0.226284150261,
          "distance_to_default": 4.615175440698,
          "physical_default_probability": 1.963817e-06,
          "risk_neutral_default_probability": 3.686975e-06,
          "iterations": 2,
          "residual": 9e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 33,
        "value": 4.643275187958,
        "value_label": "4.6433 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.6433 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 145.5,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 223.135631575485,
          "asset_volatility": 0.228224663381,
          "distance_to_default": 4.643275187958,
          "physical_default_probability": 1.714646e-06,
          "risk_neutral_default_probability": 3.213599e-06,
          "iterations": 2,
          "residual": 7e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 34,
        "value": 4.671091875297,
        "value_label": "4.6711 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.6711 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 149.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 226.635632968907,
          "asset_volatility": 0.230105244961,
          "distance_to_default": 4.671091875297,
          "physical_default_probability": 1.498014e-06,
          "risk_neutral_default_probability": 2.803165e-06,
          "iterations": 2,
          "residual": 5e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 35,
        "value": 4.698629811942,
        "value_label": "4.6986 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.6986 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 152.5,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 230.135634182896,
          "asset_volatility": 0.231928628866,
          "distance_to_default": 4.698629811942,
          "physical_default_probability": 1.309563e-06,
          "risk_neutral_default_probability": 2.447017e-06,
          "iterations": 2,
          "residual": 4e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 36,
        "value": 4.725893350864,
        "value_label": "4.7259 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.7259 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 156.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 233.635635241084,
          "asset_volatility": 0.233697385202,
          "distance_to_default": 4.725893350864,
          "physical_default_probability": 1.145529e-06,
          "risk_neutral_default_probability": 2.137725e-06,
          "iterations": 2,
          "residual": 3e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 37,
        "value": 4.752886866289,
        "value_label": "4.7529 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.7529 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 159.5,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 237.135636163936,
          "asset_volatility": 0.235413932403,
          "distance_to_default": 4.752886866289,
          "physical_default_probability": 1.002663e-06,
          "risk_neutral_default_probability": 1.868914e-06,
          "iterations": 2,
          "residual": 2e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 38,
        "value": 4.779614735042,
        "value_label": "4.7796 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.7796 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 163.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 240.635636969176,
          "asset_volatility": 0.237080548248,
          "distance_to_default": 4.779614735042,
          "physical_default_probability": 8.78157e-07,
          "risk_neutral_default_probability": 1.635102e-06,
          "iterations": 2,
          "residual": 2e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 39,
        "value": 4.806081321093,
        "value_label": "4.8061 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.8061 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 166.5,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 244.135637672163,
          "asset_volatility": 0.238699379938,
          "distance_to_default": 4.806081321093,
          "physical_default_probability": 7.69587e-07,
          "risk_neutral_default_probability": 1.431577e-06,
          "iterations": 2,
          "residual": 1e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 40,
        "value": 4.832290962808,
        "value_label": "4.8323 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.8323 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 170.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 247.635638286208,
          "asset_volatility": 0.240272453319,
          "distance_to_default": 4.832290962808,
          "physical_default_probability": 6.74854e-07,
          "risk_neutral_default_probability": 1.25428e-06,
          "iterations": 2,
          "residual": 1e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 41,
        "value": 4.858247962445,
        "value_label": "4.8582 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.8582 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 173.5,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 251.135638822853,
          "asset_volatility": 0.241801681336,
          "distance_to_default": 4.858247962445,
          "physical_default_probability": 5.92145e-07,
          "risk_neutral_default_probability": 1.099716e-06,
          "iterations": 2,
          "residual": 1e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 42,
        "value": 4.883956577569,
        "value_label": "4.8840 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.8840 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 177.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 254.635639292108,
          "asset_volatility": 0.243288871783,
          "distance_to_default": 4.883956577569,
          "physical_default_probability": 5.1989e-07,
          "risk_neutral_default_probability": 9.6487e-07,
          "iterations": 2,
          "residual": 1e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 43,
        "value": 4.909421014071,
        "value_label": "4.9094 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.9094 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 180.5,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 258.13563970266,
          "asset_volatility": 0.244735734434,
          "distance_to_default": 4.909421014071,
          "physical_default_probability": 4.56728e-07,
          "risk_neutral_default_probability": 8.4714e-07,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 44,
        "value": 4.934645420538,
        "value_label": "4.9346 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.9346 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 184.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 261.63564006205,
          "asset_volatility": 0.246143887592,
          "distance_to_default": 4.934645420538,
          "physical_default_probability": 4.01483e-07,
          "risk_neutral_default_probability": 7.4428e-07,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 45,
        "value": 4.959633883776,
        "value_label": "4.9596 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.9596 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 187.5,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 265.135640376826,
          "asset_volatility": 0.247514864126,
          "distance_to_default": 4.959633883776,
          "physical_default_probability": 3.53131e-07,
          "risk_neutral_default_probability": 6.54347e-07,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 46,
        "value": 4.984390425291,
        "value_label": "4.9844 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.9844 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 191.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 268.635640652679,
          "asset_volatility": 0.248850117035,
          "distance_to_default": 4.984390425291,
          "physical_default_probability": 3.10787e-07,
          "risk_neutral_default_probability": 5.75662e-07,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 47,
        "value": 5.008918998604,
        "value_label": "5.0089 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.0089 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 194.5,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 272.135640894555,
          "asset_volatility": 0.250151024579,
          "distance_to_default": 5.008918998604,
          "physical_default_probability": 2.73683e-07,
          "risk_neutral_default_probability": 5.06769e-07,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 48,
        "value": 5.033223487242,
        "value_label": "5.0332 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.0332 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 198.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 275.635641106757,
          "asset_volatility": 0.251418895027,
          "distance_to_default": 5.033223487242,
          "physical_default_probability": 2.4115e-07,
          "risk_neutral_default_probability": 4.4641e-07,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 49,
        "value": 5.05730770332,
        "value_label": "5.0573 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.0573 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 201.5,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 279.135641293027,
          "asset_volatility": 0.252654971039,
          "distance_to_default": 5.05730770332,
          "physical_default_probability": 2.12608e-07,
          "risk_neutral_default_probability": 3.9349e-07,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 50,
        "value": 5.08117538662,
        "value_label": "5.0812 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.0812 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 205.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 282.635641456625,
          "asset_volatility": 0.253860433733,
          "distance_to_default": 5.08117538662,
          "physical_default_probability": 1.87553e-07,
          "risk_neutral_default_probability": 3.47063e-07,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 51,
        "value": 5.104830204079,
        "value_label": "5.1048 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.1048 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 208.5,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 286.13564160039,
          "asset_volatility": 0.255036406441,
          "distance_to_default": 5.104830204079,
          "physical_default_probability": 1.65546e-07,
          "risk_neutral_default_probability": 3.06303e-07,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 52,
        "value": 5.128275749629,
        "value_label": "5.1283 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.1283 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 212.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 289.635641726795,
          "asset_volatility": 0.256183958205,
          "distance_to_default": 5.128275749629,
          "physical_default_probability": 1.46204e-07,
          "risk_neutral_default_probability": 2.70497e-07,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 53,
        "value": 5.151515544333,
        "value_label": "5.1515 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.1515 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 215.5,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 293.135641837998,
          "asset_volatility": 0.257304107014,
          "distance_to_default": 5.151515544333,
          "physical_default_probability": 1.29195e-07,
          "risk_neutral_default_probability": 2.39022e-07,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 54,
        "value": 5.174553036762,
        "value_label": "5.1746 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.1746 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 219.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 296.635641935879,
          "asset_volatility": 0.258397822817,
          "distance_to_default": 5.174553036762,
          "physical_default_probability": 1.14229e-07,
          "risk_neutral_default_probability": 2.11336e-07,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 55,
        "value": 5.197391603578,
        "value_label": "5.1974 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.1974 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 222.5,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 300.135642022083,
          "asset_volatility": 0.259466030325,
          "distance_to_default": 5.197391603578,
          "physical_default_probability": 1.01052e-07,
          "risk_neutral_default_probability": 1.86967e-07,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 56,
        "value": 5.22003455029,
        "value_label": "5.2200 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.2200 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 226.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 303.635642098042,
          "asset_volatility": 0.260509611613,
          "distance_to_default": 5.22003455029,
          "physical_default_probability": 8.9445e-08,
          "risk_neutral_default_probability": 1.65506e-07,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 57,
        "value": 5.242485112141,
        "value_label": "5.2425 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.2425 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 229.5,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 307.13564216501,
          "asset_volatility": 0.261529408552,
          "distance_to_default": 5.242485112141,
          "physical_default_probability": 7.9214e-08,
          "risk_neutral_default_probability": 1.46593e-07,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 58,
        "value": 5.26474645512,
        "value_label": "5.2647 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.2647 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 233.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 310.635642224083,
          "asset_volatility": 0.262526225076,
          "distance_to_default": 5.26474645512,
          "physical_default_probability": 7.0191e-08,
          "risk_neutral_default_probability": 1.29916e-07,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 59,
        "value": 5.286821677052,
        "value_label": "5.2868 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.2868 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 236.5,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 314.13564227622,
          "asset_volatility": 0.26350082929,
          "distance_to_default": 5.286821677052,
          "physical_default_probability": 6.223e-08,
          "risk_neutral_default_probability": 1.15201e-07,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 60,
        "value": 5.308713808777,
        "value_label": "5.3087 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.3087 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 240.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 317.63564232226,
          "asset_volatility": 0.264453955446,
          "distance_to_default": 5.308713808777,
          "physical_default_probability": 5.5201e-08,
          "risk_neutral_default_probability": 1.0221e-07,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      }
    ]
  },
  {
    "name": "Threshold or boundary",
    "description": "Synthetic threshold or boundary sweep; only declared fields change while the topic contract remains fixed.",
    "canonical_step": 30,
    "summary": {
      "focus_step": 30,
      "focus_kind": "comparison",
      "canonical_output_match": false,
      "state_counts": {
        "converged": 61
      },
      "value_min": 3.208356242938,
      "value_max": 5.561153280066,
      "segments": [
        {
          "start_step": 0,
          "end_step": 60,
          "state": "converged",
          "decision": "merton-equity-system-solved",
          "start_value_label": "3.2084 sigma",
          "end_value_label": "5.5612 sigma"
        }
      ]
    },
    "states": [
      {
        "step": 0,
        "value": 3.208356242938,
        "value_label": "3.2084 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.2084 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": -0.2,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 3.208356242938,
          "physical_default_probability": 0.000667480144,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 1,
        "value": 3.24756952689,
        "value_label": "3.2476 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.2476 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": -0.191666666667,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 3.24756952689,
          "physical_default_probability": 0.000581976113,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 2,
        "value": 3.286782810842,
        "value_label": "3.2868 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.2868 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": -0.183333333333,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 3.286782810842,
          "physical_default_probability": 0.000506694798,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 3,
        "value": 3.325996094795,
        "value_label": "3.3260 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.3260 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": -0.175,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 3.325996094795,
          "physical_default_probability": 0.000440515815,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 4,
        "value": 3.365209378747,
        "value_label": "3.3652 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.3652 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": -0.166666666667,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 3.365209378747,
          "physical_default_probability": 0.000382427971,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 5,
        "value": 3.404422662699,
        "value_label": "3.4044 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.4044 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": -0.158333333333,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 3.404422662699,
          "physical_default_probability": 0.000331520363,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 6,
        "value": 3.443635946651,
        "value_label": "3.4436 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.4436 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": -0.15,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 3.443635946651,
          "physical_default_probability": 0.000286973982,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 7,
        "value": 3.482849230603,
        "value_label": "3.4828 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.4828 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": -0.141666666667,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 3.482849230603,
          "physical_default_probability": 0.000248053839,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 8,
        "value": 3.522062514555,
        "value_label": "3.5221 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.5221 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": -0.133333333333,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 3.522062514555,
          "physical_default_probability": 0.000214101577,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 9,
        "value": 3.561275798507,
        "value_label": "3.5613 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.5613 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": -0.125,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 3.561275798507,
          "physical_default_probability": 0.000184528585,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 10,
        "value": 3.600489082459,
        "value_label": "3.6005 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.6005 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": -0.116666666667,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 3.600489082459,
          "physical_default_probability": 0.000158809583,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 11,
        "value": 3.639702366412,
        "value_label": "3.6397 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.6397 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": -0.108333333333,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 3.639702366412,
          "physical_default_probability": 0.000136476677,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 12,
        "value": 3.678915650364,
        "value_label": "3.6789 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.6789 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": -0.1,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 3.678915650364,
          "physical_default_probability": 0.000117113857,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 13,
        "value": 3.718128934316,
        "value_label": "3.7181 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.7181 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": -0.091666666667,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 3.718128934316,
          "physical_default_probability": 0.000100351916,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 14,
        "value": 3.757342218268,
        "value_label": "3.7573 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.7573 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": -0.083333333333,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 3.757342218268,
          "physical_default_probability": 8.5863788e-05,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 15,
        "value": 3.79655550222,
        "value_label": "3.7966 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.7966 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": -0.075,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 3.79655550222,
          "physical_default_probability": 7.3360263e-05,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 16,
        "value": 3.835768786172,
        "value_label": "3.8358 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.8358 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": -0.066666666667,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 3.835768786172,
          "physical_default_probability": 6.2586063e-05,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 17,
        "value": 3.874982070124,
        "value_label": "3.8750 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.8750 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": -0.058333333333,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 3.874982070124,
          "physical_default_probability": 5.3316275e-05,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 18,
        "value": 3.914195354076,
        "value_label": "3.9142 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.9142 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": -0.05,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 3.914195354076,
          "physical_default_probability": 4.5353089e-05,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 19,
        "value": 3.953408638029,
        "value_label": "3.9534 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.9534 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": -0.041666666667,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 3.953408638029,
          "physical_default_probability": 3.8522845e-05,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 20,
        "value": 3.992621921981,
        "value_label": "3.9926 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.9926 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": -0.033333333333,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 3.992621921981,
          "physical_default_probability": 3.2673357e-05,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 21,
        "value": 4.031835205933,
        "value_label": "4.0318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.0318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": -0.025,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.031835205933,
          "physical_default_probability": 2.7671495e-05,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 22,
        "value": 4.071048489885,
        "value_label": "4.0710 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.0710 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": -0.016666666667,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.071048489885,
          "physical_default_probability": 2.3401002e-05,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 23,
        "value": 4.110261773837,
        "value_label": "4.1103 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.1103 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": -0.008333333333,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.110261773837,
          "physical_default_probability": 1.9760541e-05,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 24,
        "value": 4.149475057789,
        "value_label": "4.1495 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.1495 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.0,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.149475057789,
          "physical_default_probability": 1.666193e-05,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 25,
        "value": 4.188688341741,
        "value_label": "4.1887 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.1887 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.008333333333,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.188688341741,
          "physical_default_probability": 1.402857e-05,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 26,
        "value": 4.227901625693,
        "value_label": "4.2279 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.2279 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.016666666667,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.227901625693,
          "physical_default_probability": 1.1794044e-05,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 27,
        "value": 4.267114909646,
        "value_label": "4.2671 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.2671 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.025,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.267114909646,
          "physical_default_probability": 9.900859e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 28,
        "value": 4.306328193598,
        "value_label": "4.3063 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.3063 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.033333333333,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.306328193598,
          "physical_default_probability": 8.299337e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 29,
        "value": 4.34554147755,
        "value_label": "4.3455 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.3455 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.041666666667,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.34554147755,
          "physical_default_probability": 6.946626e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 30,
        "value": 4.384754761502,
        "value_label": "4.3848 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.3848 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.05,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.384754761502,
          "physical_default_probability": 5.805826e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 31,
        "value": 4.423968045454,
        "value_label": "4.4240 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4240 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.058333333333,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.423968045454,
          "physical_default_probability": 4.845218e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 32,
        "value": 4.463181329406,
        "value_label": "4.4632 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4632 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.066666666667,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.463181329406,
          "physical_default_probability": 4.037583e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 33,
        "value": 4.502394613358,
        "value_label": "4.5024 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.5024 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.075,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.502394613358,
          "physical_default_probability": 3.359604e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 34,
        "value": 4.54160789731,
        "value_label": "4.5416 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.5416 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.083333333333,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.54160789731,
          "physical_default_probability": 2.79134e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 35,
        "value": 4.580821181263,
        "value_label": "4.5808 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.5808 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.091666666667,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.580821181263,
          "physical_default_probability": 2.315769e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 36,
        "value": 4.620034465215,
        "value_label": "4.6200 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.6200 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.1,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.620034465215,
          "physical_default_probability": 1.918382e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 37,
        "value": 4.659247749167,
        "value_label": "4.6592 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.6592 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.108333333333,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.659247749167,
          "physical_default_probability": 1.586835e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 38,
        "value": 4.698461033119,
        "value_label": "4.6985 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.6985 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.116666666667,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.698461033119,
          "physical_default_probability": 1.310646e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 39,
        "value": 4.737674317071,
        "value_label": "4.7377 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.7377 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.125,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.737674317071,
          "physical_default_probability": 1.080924e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 40,
        "value": 4.776887601023,
        "value_label": "4.7769 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.7769 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.133333333333,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.776887601023,
          "physical_default_probability": 8.90146e-07,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 41,
        "value": 4.816100884975,
        "value_label": "4.8161 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.8161 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.141666666667,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.816100884975,
          "physical_default_probability": 7.31953e-07,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 42,
        "value": 4.855314168927,
        "value_label": "4.8553 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.8553 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.15,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.855314168927,
          "physical_default_probability": 6.0098e-07,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 43,
        "value": 4.89452745288,
        "value_label": "4.8945 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.8945 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.158333333333,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.89452745288,
          "physical_default_probability": 4.92711e-07,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 44,
        "value": 4.933740736832,
        "value_label": "4.9337 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.9337 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.166666666667,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.933740736832,
          "physical_default_probability": 4.03348e-07,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 45,
        "value": 4.972954020784,
        "value_label": "4.9730 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.9730 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.175,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.972954020784,
          "physical_default_probability": 3.29702e-07,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 46,
        "value": 5.012167304736,
        "value_label": "5.0122 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.0122 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.183333333333,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 5.012167304736,
          "physical_default_probability": 2.69102e-07,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 47,
        "value": 5.051380588688,
        "value_label": "5.0514 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.0514 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.191666666667,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 5.051380588688,
          "physical_default_probability": 2.19314e-07,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 48,
        "value": 5.09059387264,
        "value_label": "5.0906 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.0906 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.2,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 5.09059387264,
          "physical_default_probability": 1.78472e-07,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 49,
        "value": 5.129807156592,
        "value_label": "5.1298 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.1298 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.208333333333,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 5.129807156592,
          "physical_default_probability": 1.4502e-07,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 50,
        "value": 5.169020440544,
        "value_label": "5.1690 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.1690 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.216666666667,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 5.169020440544,
          "physical_default_probability": 1.17662e-07,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 51,
        "value": 5.208233724497,
        "value_label": "5.2082 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.2082 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.225,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 5.208233724497,
          "physical_default_probability": 9.5323e-08,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 52,
        "value": 5.247447008449,
        "value_label": "5.2474 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.2474 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.233333333333,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 5.247447008449,
          "physical_default_probability": 7.7111e-08,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 53,
        "value": 5.286660292401,
        "value_label": "5.2867 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.2867 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.241666666667,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 5.286660292401,
          "physical_default_probability": 6.2285e-08,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 54,
        "value": 5.325873576353,
        "value_label": "5.3259 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.3259 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.25,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 5.325873576353,
          "physical_default_probability": 5.0234e-08,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 55,
        "value": 5.365086860305,
        "value_label": "5.3651 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.3651 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.258333333333,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 5.365086860305,
          "physical_default_probability": 4.0455e-08,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 56,
        "value": 5.404300144257,
        "value_label": "5.4043 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.4043 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.266666666667,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 5.404300144257,
          "physical_default_probability": 3.2531e-08,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 57,
        "value": 5.443513428209,
        "value_label": "5.4435 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.4435 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.275,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 5.443513428209,
          "physical_default_probability": 2.612e-08,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 58,
        "value": 5.482726712161,
        "value_label": "5.4827 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.4827 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.283333333333,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 5.482726712161,
          "physical_default_probability": 2.0941e-08,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 59,
        "value": 5.521939996114,
        "value_label": "5.5219 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.5219 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.291666666667,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 5.521939996114,
          "physical_default_probability": 1.6764e-08,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 60,
        "value": 5.561153280066,
        "value_label": "5.5612 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.5612 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.3,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 5.561153280066,
          "physical_default_probability": 1.34e-08,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      }
    ]
  },
  {
    "name": "Sensitivity",
    "description": "Synthetic sensitivity sweep; only declared fields change while the topic contract remains fixed.",
    "canonical_step": 30,
    "summary": {
      "focus_step": 30,
      "focus_kind": "comparison",
      "canonical_output_match": false,
      "state_counts": {
        "converged": 61
      },
      "value_min": 4.18510562052,
      "value_max": 4.62102228231,
      "segments": [
        {
          "start_step": 0,
          "end_step": 60,
          "state": "converged",
          "decision": "merton-equity-system-solved",
          "start_value_label": "4.6210 sigma",
          "end_value_label": "4.1851 sigma"
        }
      ]
    },
    "states": [
      {
        "step": 0,
        "value": 4.62102228231,
        "value_label": "4.6210 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.6210 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": -0.02,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 201.616067505517,
          "asset_volatility": 0.208317644653,
          "distance_to_default": 4.62102228231,
          "physical_default_probability": 1.909269e-06,
          "risk_neutral_default_probability": 1.1326641e-05,
          "iterations": 2,
          "residual": 9.1e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 1,
        "value": 4.613235430529,
        "value_label": "4.6132 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.6132 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": -0.018,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 201.452998850953,
          "asset_volatility": 0.208486260304,
          "distance_to_default": 4.613235430529,
          "physical_default_probability": 1.982244e-06,
          "risk_neutral_default_probability": 1.1220381e-05,
          "iterations": 2,
          "residual": 8.9e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 2,
        "value": 4.605467131626,
        "value_label": "4.6055 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.6055 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": -0.016,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 201.290256004488,
          "asset_volatility": 0.208654811512,
          "distance_to_default": 4.605467131626,
          "physical_default_probability": 2.057705e-06,
          "risk_neutral_default_probability": 1.111495e-05,
          "iterations": 2,
          "residual": 8.7e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 3,
        "value": 4.597717338783,
        "value_label": "4.5977 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.5977 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": -0.014,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 201.127838315183,
          "asset_volatility": 0.208823297976,
          "distance_to_default": 4.597717338783,
          "physical_default_probability": 2.135725e-06,
          "risk_neutral_default_probability": 1.1010342e-05,
          "iterations": 2,
          "residual": 8.6e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 4,
        "value": 4.589986005306,
        "value_label": "4.5900 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.5900 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": -0.012,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 200.965745133396,
          "asset_volatility": 0.208991719396,
          "distance_to_default": 4.589986005306,
          "physical_default_probability": 2.216379e-06,
          "risk_neutral_default_probability": 1.0906554e-05,
          "iterations": 2,
          "residual": 8.4e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 5,
        "value": 4.582273084623,
        "value_label": "4.5823 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.5823 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": -0.01,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 200.803975810784,
          "asset_volatility": 0.209160075473,
          "distance_to_default": 4.582273084623,
          "physical_default_probability": 2.299743e-06,
          "risk_neutral_default_probability": 1.0803579e-05,
          "iterations": 2,
          "residual": 8.2e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 6,
        "value": 4.574578530283,
        "value_label": "4.5746 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.5746 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": -0.008,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 200.642529700302,
          "asset_volatility": 0.209328365908,
          "distance_to_default": 4.574578530283,
          "physical_default_probability": 2.385898e-06,
          "risk_neutral_default_probability": 1.0701414e-05,
          "iterations": 2,
          "residual": 8.1e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 7,
        "value": 4.566902295955,
        "value_label": "4.5669 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.5669 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": -0.006,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 200.481406156193,
          "asset_volatility": 0.209496590402,
          "distance_to_default": 4.566902295955,
          "physical_default_probability": 2.474923e-06,
          "risk_neutral_default_probability": 1.0600054e-05,
          "iterations": 2,
          "residual": 7.9e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 8,
        "value": 4.559244335432,
        "value_label": "4.5592 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.5592 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": -0.004,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 200.320604533994,
          "asset_volatility": 0.209664748658,
          "distance_to_default": 4.559244335432,
          "physical_default_probability": 2.566901e-06,
          "risk_neutral_default_probability": 1.0499494e-05,
          "iterations": 2,
          "residual": 7.8e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 9,
        "value": 4.551604602625,
        "value_label": "4.5516 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.5516 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": -0.002,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 200.160124190528,
          "asset_volatility": 0.209832840379,
          "distance_to_default": 4.551604602625,
          "physical_default_probability": 2.661916e-06,
          "risk_neutral_default_probability": 1.0399729e-05,
          "iterations": 2,
          "residual": 7.6e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 10,
        "value": 4.543983051567,
        "value_label": "4.5440 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.5440 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": -0.0,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 199.999964483902,
          "asset_volatility": 0.210000865267,
          "distance_to_default": 4.543983051567,
          "physical_default_probability": 2.760055e-06,
          "risk_neutral_default_probability": 1.0300754e-05,
          "iterations": 2,
          "residual": 7.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 11,
        "value": 4.53637963641,
        "value_label": "4.5364 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.5364 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.002,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 199.840124773507,
          "asset_volatility": 0.210168823026,
          "distance_to_default": 4.53637963641,
          "physical_default_probability": 2.861406e-06,
          "risk_neutral_default_probability": 1.0202566e-05,
          "iterations": 2,
          "residual": 7.3e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 12,
        "value": 4.528794311426,
        "value_label": "4.5288 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.5288 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.004,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 199.680604420013,
          "asset_volatility": 0.210336713361,
          "distance_to_default": 4.528794311426,
          "physical_default_probability": 2.966061e-06,
          "risk_neutral_default_probability": 1.0105158e-05,
          "iterations": 2,
          "residual": 7.2e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 13,
        "value": 4.521227031007,
        "value_label": "4.5212 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.5212 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.006,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 199.521402785367,
          "asset_volatility": 0.210504535975,
          "distance_to_default": 4.521227031007,
          "physical_default_probability": 3.07411e-06,
          "risk_neutral_default_probability": 1.0008527e-05,
          "iterations": 2,
          "residual": 7e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 14,
        "value": 4.513677749664,
        "value_label": "4.5137 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.5137 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.008,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 199.362519232792,
          "asset_volatility": 0.210672290575,
          "distance_to_default": 4.513677749664,
          "physical_default_probability": 3.18565e-06,
          "risk_neutral_default_probability": 9.912667e-06,
          "iterations": 2,
          "residual": 6.9e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 15,
        "value": 4.506146422026,
        "value_label": "4.5061 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.5061 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.01,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 199.203953126783,
          "asset_volatility": 0.210839976865,
          "distance_to_default": 4.506146422026,
          "physical_default_probability": 3.300777e-06,
          "risk_neutral_default_probability": 9.817575e-06,
          "iterations": 2,
          "residual": 6.7e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 16,
        "value": 4.498633002841,
        "value_label": "4.4986 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4986 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.012,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 199.045703833102,
          "asset_volatility": 0.211007594553,
          "distance_to_default": 4.498633002841,
          "physical_default_probability": 3.41959e-06,
          "risk_neutral_default_probability": 9.723245e-06,
          "iterations": 2,
          "residual": 6.6e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 17,
        "value": 4.491137446975,
        "value_label": "4.4911 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4911 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.014,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 198.887770718781,
          "asset_volatility": 0.211175143344,
          "distance_to_default": 4.491137446975,
          "physical_default_probability": 3.542191e-06,
          "risk_neutral_default_probability": 9.629673e-06,
          "iterations": 2,
          "residual": 6.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 18,
        "value": 4.483659709413,
        "value_label": "4.4837 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4837 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.016,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 198.730153152116,
          "asset_volatility": 0.211342622946,
          "distance_to_default": 4.483659709413,
          "physical_default_probability": 3.668682e-06,
          "risk_neutral_default_probability": 9.536854e-06,
          "iterations": 2,
          "residual": 6.4e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 19,
        "value": 4.476199745255,
        "value_label": "4.4762 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4762 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.018,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 198.572850502665,
          "asset_volatility": 0.211510033066,
          "distance_to_default": 4.476199745255,
          "physical_default_probability": 3.79917e-06,
          "risk_neutral_default_probability": 9.444784e-06,
          "iterations": 2,
          "residual": 6.2e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 20,
        "value": 4.468757509722,
        "value_label": "4.4688 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4688 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.02,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 198.415862141244,
          "asset_volatility": 0.211677373414,
          "distance_to_default": 4.468757509722,
          "physical_default_probability": 3.933763e-06,
          "risk_neutral_default_probability": 9.353458e-06,
          "iterations": 2,
          "residual": 6.1e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 21,
        "value": 4.461332958148,
        "value_label": "4.4613 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4613 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.022,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 198.259187439927,
          "asset_volatility": 0.211844643697,
          "distance_to_default": 4.461332958148,
          "physical_default_probability": 4.072571e-06,
          "risk_neutral_default_probability": 9.262872e-06,
          "iterations": 2,
          "residual": 6e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 22,
        "value": 4.453926045986,
        "value_label": "4.4539 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4539 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.024,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 198.102825772044,
          "asset_volatility": 0.212011843626,
          "distance_to_default": 4.453926045986,
          "physical_default_probability": 4.215708e-06,
          "risk_neutral_default_probability": 9.17302e-06,
          "iterations": 2,
          "residual": 5.9e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 23,
        "value": 4.446536728806,
        "value_label": "4.4465 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4465 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.026,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.946776512175,
          "asset_volatility": 0.212178972909,
          "distance_to_default": 4.446536728806,
          "physical_default_probability": 4.363288e-06,
          "risk_neutral_default_probability": 9.083899e-06,
          "iterations": 2,
          "residual": 5.7e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 24,
        "value": 4.439164962292,
        "value_label": "4.4392 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4392 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.028,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.79103903615,
          "asset_volatility": 0.212346031257,
          "distance_to_default": 4.439164962292,
          "physical_default_probability": 4.515429e-06,
          "risk_neutral_default_probability": 8.995504e-06,
          "iterations": 2,
          "residual": 5.6e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 25,
        "value": 4.431810702245,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702245,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 26,
        "value": 4.42447390458,
        "value_label": "4.4245 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4245 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.032,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.480496945185,
          "asset_volatility": 0.212679933994,
          "distance_to_default": 4.42447390458,
          "physical_default_probability": 4.833879e-06,
          "risk_neutral_default_probability": 8.820874e-06,
          "iterations": 2,
          "residual": 5.4e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 27,
        "value": 4.417154525331,
        "value_label": "4.4172 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4172 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.034,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.325691088129,
          "asset_volatility": 0.212846777806,
          "distance_to_default": 4.417154525331,
          "physical_default_probability": 5.000437e-06,
          "risk_neutral_default_probability": 8.73463e-06,
          "iterations": 2,
          "residual": 5.3e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 28,
        "value": 4.409852520641,
        "value_label": "4.4099 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4099 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.036,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.171194530684,
          "asset_volatility": 0.21301354953,
          "distance_to_default": 4.409852520641,
          "physical_default_probability": 5.172052e-06,
          "risk_neutral_default_probability": 8.649094e-06,
          "iterations": 2,
          "residual": 5.2e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 29,
        "value": 4.402567846774,
        "value_label": "4.4026 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4026 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.038,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.017006654887,
          "asset_volatility": 0.213180248878,
          "distance_to_default": 4.402567846774,
          "physical_default_probability": 5.348856e-06,
          "risk_neutral_default_probability": 8.564262e-06,
          "iterations": 2,
          "residual": 5.1e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 30,
        "value": 4.395300460102,
        "value_label": "4.3953 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.3953 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.04,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 196.863126844015,
          "asset_volatility": 0.213346875566,
          "distance_to_default": 4.395300460102,
          "physical_default_probability": 5.530982e-06,
          "risk_neutral_default_probability": 8.480129e-06,
          "iterations": 2,
          "residual": 5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 31,
        "value": 4.388050317117,
        "value_label": "4.3881 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.3881 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.042,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 196.709554482574,
          "asset_volatility": 0.213513429306,
          "distance_to_default": 4.388050317117,
          "physical_default_probability": 5.718566e-06,
          "risk_neutral_default_probability": 8.396691e-06,
          "iterations": 2,
          "residual": 4.9e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 32,
        "value": 4.380817374419,
        "value_label": "4.3808 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.3808 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.044,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 196.5562889563,
          "asset_volatility": 0.213679909814,
          "distance_to_default": 4.380817374419,
          "physical_default_probability": 5.911747e-06,
          "risk_neutral_default_probability": 8.313943e-06,
          "iterations": 2,
          "residual": 4.8e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 33,
        "value": 4.373601588725,
        "value_label": "4.3736 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.3736 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.046,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 196.403329652157,
          "asset_volatility": 0.213846316805,
          "distance_to_default": 4.373601588725,
          "physical_default_probability": 6.110667e-06,
          "risk_neutral_default_probability": 8.231881e-06,
          "iterations": 2,
          "residual": 4.7e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 34,
        "value": 4.366402916865,
        "value_label": "4.3664 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.3664 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.048,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 196.250675958333,
          "asset_volatility": 0.214012649994,
          "distance_to_default": 4.366402916865,
          "physical_default_probability": 6.315469e-06,
          "risk_neutral_default_probability": 8.150501e-06,
          "iterations": 2,
          "residual": 4.6e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 35,
        "value": 4.35922131578,
        "value_label": "4.3592 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.3592 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.05,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 196.09832726424,
          "asset_volatility": 0.214178909097,
          "distance_to_default": 4.35922131578,
          "physical_default_probability": 6.526303e-06,
          "risk_neutral_default_probability": 8.069798e-06,
          "iterations": 2,
          "residual": 4.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 36,
        "value": 4.352056742524,
        "value_label": "4.3521 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.3521 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.052,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 195.946282960507,
          "asset_volatility": 0.214345093832,
          "distance_to_default": 4.352056742524,
          "physical_default_probability": 6.743317e-06,
          "risk_neutral_default_probability": 7.989769e-06,
          "iterations": 2,
          "residual": 4.4e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 37,
        "value": 4.344909154265,
        "value_label": "4.3449 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.3449 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.054,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 195.794542438982,
          "asset_volatility": 0.214511203917,
          "distance_to_default": 4.344909154265,
          "physical_default_probability": 6.966666e-06,
          "risk_neutral_default_probability": 7.910408e-06,
          "iterations": 2,
          "residual": 4.3e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 38,
        "value": 4.33777850828,
        "value_label": "4.3378 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.3378 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.056,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 195.643105092729,
          "asset_volatility": 0.214677239068,
          "distance_to_default": 4.33777850828,
          "physical_default_probability": 7.196505e-06,
          "risk_neutral_default_probability": 7.831711e-06,
          "iterations": 2,
          "residual": 4.2e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 39,
        "value": 4.330664761961,
        "value_label": "4.3307 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.3307 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.058,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 195.491970316023,
          "asset_volatility": 0.214843199005,
          "distance_to_default": 4.330664761961,
          "physical_default_probability": 7.432993e-06,
          "risk_neutral_default_probability": 7.753674e-06,
          "iterations": 2,
          "residual": 4.1e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 40,
        "value": 4.323567872807,
        "value_label": "4.3236 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.3236 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.06,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 195.341137504348,
          "asset_volatility": 0.215009083446,
          "distance_to_default": 4.323567872807,
          "physical_default_probability": 7.676294e-06,
          "risk_neutral_default_probability": 7.676294e-06,
          "iterations": 2,
          "residual": 4.1e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 41,
        "value": 4.316487798433,
        "value_label": "4.3165 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.3165 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.062,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 195.1906060544,
          "asset_volatility": 0.215174892111,
          "distance_to_default": 4.316487798433,
          "physical_default_probability": 7.926572e-06,
          "risk_neutral_default_probability": 7.599565e-06,
          "iterations": 2,
          "residual": 4e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 42,
        "value": 4.30942449656,
        "value_label": "4.3094 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.3094 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.064,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 195.040375364075,
          "asset_volatility": 0.215340624721,
          "distance_to_default": 4.30942449656,
          "physical_default_probability": 8.183996e-06,
          "risk_neutral_default_probability": 7.523483e-06,
          "iterations": 2,
          "residual": 3.9e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 43,
        "value": 4.302377925023,
        "value_label": "4.3024 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.3024 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.066,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 194.890444832476,
          "asset_volatility": 0.215506280996,
          "distance_to_default": 4.302377925023,
          "physical_default_probability": 8.448739e-06,
          "risk_neutral_default_probability": 7.448045e-06,
          "iterations": 2,
          "residual": 3.8e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 44,
        "value": 4.295348041766,
        "value_label": "4.2953 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.2953 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.068,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 194.740813859905,
          "asset_volatility": 0.215671860658,
          "distance_to_default": 4.295348041766,
          "physical_default_probability": 8.720974e-06,
          "risk_neutral_default_probability": 7.373245e-06,
          "iterations": 2,
          "residual": 3.7e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 45,
        "value": 4.288334804843,
        "value_label": "4.2883 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.2883 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.07,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 194.591481847861,
          "asset_volatility": 0.215837363428,
          "distance_to_default": 4.288334804843,
          "physical_default_probability": 9.00088e-06,
          "risk_neutral_default_probability": 7.29908e-06,
          "iterations": 2,
          "residual": 3.6e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 46,
        "value": 4.281338172416,
        "value_label": "4.2813 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.2813 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.072,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 194.44244819904,
          "asset_volatility": 0.216002789028,
          "distance_to_default": 4.281338172416,
          "physical_default_probability": 9.28864e-06,
          "risk_neutral_default_probability": 7.225546e-06,
          "iterations": 2,
          "residual": 3.6e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 47,
        "value": 4.274358102759,
        "value_label": "4.2744 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.2744 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.074,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 194.293712317332,
          "asset_volatility": 0.216168137183,
          "distance_to_default": 4.274358102759,
          "physical_default_probability": 9.584437e-06,
          "risk_neutral_default_probability": 7.152638e-06,
          "iterations": 2,
          "residual": 3.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 48,
        "value": 4.267394554253,
        "value_label": "4.2674 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.2674 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.076,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 194.145273607816,
          "asset_volatility": 0.216333407615,
          "distance_to_default": 4.267394554253,
          "physical_default_probability": 9.88846e-06,
          "risk_neutral_default_probability": 7.080353e-06,
          "iterations": 2,
          "residual": 3.4e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 49,
        "value": 4.260447485389,
        "value_label": "4.2604 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.2604 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.078,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 193.997131476761,
          "asset_volatility": 0.216498600048,
          "distance_to_default": 4.260447485389,
          "physical_default_probability": 1.0200901e-05,
          "risk_neutral_default_probability": 7.008686e-06,
          "iterations": 2,
          "residual": 3.4e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 50,
        "value": 4.253516854765,
        "value_label": "4.2535 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.2535 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.08,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 193.849285331621,
          "asset_volatility": 0.216663714208,
          "distance_to_default": 4.253516854765,
          "physical_default_probability": 1.0521955e-05,
          "risk_neutral_default_probability": 6.937633e-06,
          "iterations": 2,
          "residual": 3.3e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 51,
        "value": 4.246602621089,
        "value_label": "4.2466 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.2466 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.082,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 193.701734581034,
          "asset_volatility": 0.21682874982,
          "distance_to_default": 4.246602621089,
          "physical_default_probability": 1.085182e-05,
          "risk_neutral_default_probability": 6.86719e-06,
          "iterations": 2,
          "residual": 3.2e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 52,
        "value": 4.239704743176,
        "value_label": "4.2397 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.2397 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.084,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 193.554478634822,
          "asset_volatility": 0.216993706609,
          "distance_to_default": 4.239704743176,
          "physical_default_probability": 1.1190699e-05,
          "risk_neutral_default_probability": 6.797352e-06,
          "iterations": 2,
          "residual": 3.1e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 53,
        "value": 4.232823179949,
        "value_label": "4.2328 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.2328 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.086,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 193.407516903982,
          "asset_volatility": 0.217158584302,
          "distance_to_default": 4.232823179949,
          "physical_default_probability": 1.1538797e-05,
          "risk_neutral_default_probability": 6.728117e-06,
          "iterations": 2,
          "residual": 3.1e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 54,
        "value": 4.225957890437,
        "value_label": "4.2260 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.2260 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.088,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 193.26084880069,
          "asset_volatility": 0.217323382626,
          "distance_to_default": 4.225957890437,
          "physical_default_probability": 1.1896324e-05,
          "risk_neutral_default_probability": 6.65948e-06,
          "iterations": 2,
          "residual": 3e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 55,
        "value": 4.219108833777,
        "value_label": "4.2191 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.2191 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.09,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 193.114473738297,
          "asset_volatility": 0.217488101309,
          "distance_to_default": 4.219108833777,
          "physical_default_probability": 1.2263493e-05,
          "risk_neutral_default_probability": 6.591436e-06,
          "iterations": 2,
          "residual": 3e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 56,
        "value": 4.212275969213,
        "value_label": "4.2123 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.2123 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.092,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 192.968391131324,
          "asset_volatility": 0.217652740078,
          "distance_to_default": 4.212275969213,
          "physical_default_probability": 1.264052e-05,
          "risk_neutral_default_probability": 6.523982e-06,
          "iterations": 2,
          "residual": 2.9e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 57,
        "value": 4.205459256096,
        "value_label": "4.2055 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.2055 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.094,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 192.822600395463,
          "asset_volatility": 0.217817298663,
          "distance_to_default": 4.205459256096,
          "physical_default_probability": 1.3027626e-05,
          "risk_neutral_default_probability": 6.457114e-06,
          "iterations": 2,
          "residual": 2.8e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 58,
        "value": 4.198658653883,
        "value_label": "4.1987 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.1987 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.096,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 192.677100947573,
          "asset_volatility": 0.217981776794,
          "distance_to_default": 4.198658653883,
          "physical_default_probability": 1.3425035e-05,
          "risk_neutral_default_probability": 6.390828e-06,
          "iterations": 2,
          "residual": 2.8e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 59,
        "value": 4.191874122134,
        "value_label": "4.1919 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.1919 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.098,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 192.531892205679,
          "asset_volatility": 0.218146174199,
          "distance_to_default": 4.191874122134,
          "physical_default_probability": 1.3832975e-05,
          "risk_neutral_default_probability": 6.32512e-06,
          "iterations": 2,
          "residual": 2.7e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 60,
        "value": 4.18510562052,
        "value_label": "4.1851 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.1851 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.1,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 192.386973588966,
          "asset_volatility": 0.21831049061,
          "distance_to_default": 4.18510562052,
          "physical_default_probability": 1.4251677e-05,
          "risk_neutral_default_probability": 6.259985e-06,
          "iterations": 2,
          "residual": 2.7e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      }
    ]
  },
  {
    "name": "Scale or horizon",
    "description": "Synthetic scale or horizon sweep; only declared fields change while the topic contract remains fixed.",
    "canonical_step": 30,
    "summary": {
      "focus_step": 30,
      "focus_kind": "comparison",
      "canonical_output_match": false,
      "state_counts": {
        "converged": 61
      },
      "value_min": 2.618066550926,
      "value_max": 8.761847412459,
      "segments": [
        {
          "start_step": 0,
          "end_step": 60,
          "state": "converged",
          "decision": "merton-equity-system-solved",
          "start_value_label": "8.7618 sigma",
          "end_value_label": "2.6181 sigma"
        }
      ]
    },
    "states": [
      {
        "step": 0,
        "value": 8.761847412459,
        "value_label": "8.7618 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 8.7618 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 0.25,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 199.402244385531,
          "asset_volatility": 0.210629524905,
          "distance_to_default": 8.761847412459,
          "physical_default_probability": 0.0,
          "risk_neutral_default_probability": 0.0,
          "iterations": 1,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 1,
        "value": 8.06044290197,
        "value_label": "8.0604 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 8.0604 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 0.295833333333,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 199.293141325044,
          "asset_volatility": 0.210744834071,
          "distance_to_default": 8.06044290197,
          "physical_default_probability": 0.0,
          "risk_neutral_default_probability": 0.0,
          "iterations": 1,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 2,
        "value": 7.505792937366,
        "value_label": "7.5058 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 7.5058 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 0.341666666667,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 199.184188178177,
          "asset_volatility": 0.210860110856,
          "distance_to_default": 7.505792937366,
          "physical_default_probability": 0.0,
          "risk_neutral_default_probability": 0.0,
          "iterations": 1,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 3,
        "value": 7.053036264623,
        "value_label": "7.0530 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 7.0530 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 0.3875,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 199.075384738936,
          "asset_volatility": 0.210975355166,
          "distance_to_default": 7.053036264623,
          "physical_default_probability": 1e-12,
          "risk_neutral_default_probability": 2e-12,
          "iterations": 1,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 4,
        "value": 6.674422150194,
        "value_label": "6.6744 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 6.6744 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 0.433333333333,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 198.966730801586,
          "asset_volatility": 0.211090566906,
          "distance_to_default": 6.674422150194,
          "physical_default_probability": 1.2e-11,
          "risk_neutral_default_probability": 2.3e-11,
          "iterations": 1,
          "residual": 2e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 5,
        "value": 6.35174187673,
        "value_label": "6.3517 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 6.3517 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 0.479166666667,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 198.858226160461,
          "asset_volatility": 0.211205745994,
          "distance_to_default": 6.35174187673,
          "physical_default_probability": 1.06e-10,
          "risk_neutral_default_probability": 2.01e-10,
          "iterations": 1,
          "residual": 1.7e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 6,
        "value": 6.07248682705,
        "value_label": "6.0725 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 6.0725 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 0.525,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 198.749870609118,
          "asset_volatility": 0.211320892389,
          "distance_to_default": 6.07248682705,
          "physical_default_probability": 6.3e-10,
          "risk_neutral_default_probability": 1.189e-09,
          "iterations": 1,
          "residual": 1e-10,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 7,
        "value": 5.827742318579,
        "value_label": "5.8277 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.8277 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 0.570833333333,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 198.641663937627,
          "asset_volatility": 0.21143600619,
          "distance_to_default": 5.827742318579,
          "physical_default_probability": 2.809e-09,
          "risk_neutral_default_probability": 5.309e-09,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 8,
        "value": 5.610960576016,
        "value_label": "5.6110 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.6110 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 0.616666666667,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 198.533605925927,
          "asset_volatility": 0.211551087845,
          "distance_to_default": 5.610960576016,
          "physical_default_probability": 1.006e-08,
          "risk_neutral_default_probability": 1.9033e-08,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 9,
        "value": 5.417209677424,
        "value_label": "5.4172 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.4172 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 0.6625,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 198.425696330719,
          "asset_volatility": 0.211666138509,
          "distance_to_default": 5.417209677424,
          "physical_default_probability": 3.0268e-08,
          "risk_neutral_default_probability": 5.7318e-08,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 10,
        "value": 5.242694613064,
        "value_label": "5.2427 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.2427 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 0.708333333333,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 198.317934863639,
          "asset_volatility": 0.211781160579,
          "distance_to_default": 5.242694613064,
          "physical_default_probability": 7.9124e-08,
          "risk_neutral_default_probability": 1.49979e-07,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 11,
        "value": 5.084441128512,
        "value_label": "5.0844 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 5.0844 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 0.754166666667,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 198.210321159609,
          "asset_volatility": 0.211896158369,
          "distance_to_default": 5.084441128512,
          "physical_default_probability": 1.84355e-07,
          "risk_neutral_default_probability": 3.49772e-07,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 12,
        "value": 4.94008076307,
        "value_label": "4.9401 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.9401 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 0.8,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 198.102854735856,
          "asset_volatility": 0.212011138862,
          "distance_to_default": 4.94008076307,
          "physical_default_probability": 3.90451e-07,
          "risk_neutral_default_probability": 7.41483e-07,
          "iterations": 2,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 13,
        "value": 4.807700906252,
        "value_label": "4.8077 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.8077 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 0.845833333333,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.995534943689,
          "asset_volatility": 0.212126112474,
          "distance_to_default": 4.807700906252,
          "physical_default_probability": 7.6338e-07,
          "risk_neutral_default_probability": 1.451025e-06,
          "iterations": 2,
          "residual": 2e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 14,
        "value": 4.685737842495,
        "value_label": "4.6857 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.6857 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 0.891666666667,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.888360916295,
          "asset_volatility": 0.212241093718,
          "distance_to_default": 4.685737842495,
          "physical_default_probability": 1.394766e-06,
          "risk_neutral_default_probability": 2.653572e-06,
          "iterations": 2,
          "residual": 5e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 15,
        "value": 4.572898941541,
        "value_label": "4.5729 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.5729 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 0.9375,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.781331516337,
          "asset_volatility": 0.212356101739,
          "distance_to_default": 4.572898941541,
          "physical_default_probability": 2.405111e-06,
          "risk_neutral_default_probability": 4.579894e-06,
          "iterations": 2,
          "residual": 1.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 16,
        "value": 4.468105053081,
        "value_label": "4.4681 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4681 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 0.983333333333,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.674445287096,
          "asset_volatility": 0.212471160631,
          "distance_to_default": 4.468105053081,
          "physical_default_probability": 3.945778e-06,
          "risk_neutral_default_probability": 7.520367e-06,
          "iterations": 2,
          "residual": 4e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 17,
        "value": 4.37044718693,
        "value_label": "4.3704 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.3704 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.029166666667,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.567700410305,
          "asset_volatility": 0.212586299559,
          "distance_to_default": 4.37044718693,
          "physical_default_probability": 6.199617e-06,
          "risk_neutral_default_probability": 1.1826409e-05,
          "iterations": 2,
          "residual": 9.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 18,
        "value": 4.279153474346,
        "value_label": "4.2792 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.2792 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.075,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.461094673043,
          "asset_volatility": 0.212701552651,
          "distance_to_default": 4.279153474346,
          "physical_default_probability": 9.380274e-06,
          "risk_neutral_default_probability": 1.7909382e-05,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 19,
        "value": 4.193563647516,
        "value_label": "4.1936 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.1936 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.120833333333,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.354625445101,
          "asset_volatility": 0.212816958716,
          "distance_to_default": 4.193563647516,
          "physical_default_probability": 1.3730299e-05,
          "risk_neutral_default_probability": 2.6237206e-05,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 20,
        "value": 4.113109096714,
        "value_label": "4.1131 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.1131 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.166666666667,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.248289667344,
          "asset_volatility": 0.212932560793,
          "distance_to_default": 4.113109096714,
          "physical_default_probability": 1.9518289e-05,
          "risk_neutral_default_probability": 3.7329076e-05,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 21,
        "value": 4.037297120217,
        "value_label": "4.0373 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.0373 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.2125,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.142083850859,
          "asset_volatility": 0.213048405583,
          "distance_to_default": 4.037297120217,
          "physical_default_probability": 2.7035285e-05,
          "risk_neutral_default_probability": 5.1748728e-05,
          "iterations": 3,
          "residual": 1e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 22,
        "value": 3.965698363958,
        "value_label": "3.9657 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.9657 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.258333333333,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 197.03600408609,
          "asset_volatility": 0.213164542805,
          "distance_to_default": 3.965698363958,
          "physical_default_probability": 3.6590681e-05,
          "risk_neutral_default_probability": 7.0096726e-05,
          "iterations": 3,
          "residual": 1e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 23,
        "value": 3.897936714751,
        "value_label": "3.8979 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.8979 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.304166666667,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 196.93004606074,
          "asset_volatility": 0.213281024503,
          "distance_to_default": 3.897936714751,
          "physical_default_probability": 4.850788e-05,
          "risk_neutral_default_probability": 9.3002208e-05,
          "iterations": 3,
          "residual": 3e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 24,
        "value": 3.833681100053,
        "value_label": "3.8337 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.8337 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.35,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 196.824205085036,
          "asset_volatility": 0.213397904343,
          "distance_to_default": 3.833681100053,
          "physical_default_probability": 6.3119891e-05,
          "risk_neutral_default_probability": 0.000121114475,
          "iterations": 3,
          "residual": 6e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 25,
        "value": 3.772638783177,
        "value_label": "3.7726 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.7726 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.395833333333,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 196.718476122803,
          "asset_volatility": 0.213515236925,
          "distance_to_default": 3.772638783177,
          "physical_default_probability": 8.0765031e-05,
          "risk_neutral_default_probability": 0.00015509474,
          "iterations": 3,
          "residual": 1.2e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 26,
        "value": 3.714549841785,
        "value_label": "3.7145 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.7145 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.441666666667,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 196.61285382686,
          "asset_volatility": 0.21363307713,
          "distance_to_default": 3.714549841785,
          "physical_default_probability": 0.000101782873,
          "risk_neutral_default_probability": 0.000195608289,
          "iterations": 3,
          "residual": 2.2e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 27,
        "value": 3.659182590286,
        "value_label": "3.6592 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.6592 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.4875,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 196.507332577315,
          "asset_volatility": 0.213751479524,
          "distance_to_default": 3.659182590286,
          "physical_default_probability": 0.00012651051,
          "risk_neutral_default_probability": 0.000243317231,
          "iterations": 3,
          "residual": 4e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 28,
        "value": 3.606329760925,
        "value_label": "3.6063 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.6063 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.533333333333,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 196.401906521478,
          "asset_volatility": 0.213870497807,
          "distance_to_default": 3.606329760925,
          "physical_default_probability": 0.000155279219,
          "risk_neutral_default_probability": 0.000298873964,
          "iterations": 3,
          "residual": 7.1e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 29,
        "value": 3.555805299046,
        "value_label": "3.5558 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.5558 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.579166666667,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 196.296569614294,
          "asset_volatility": 0.213990184348,
          "distance_to_default": 3.555805299046,
          "physical_default_probability": 0.000188411537,
          "risk_neutral_default_probability": 0.000362915414,
          "iterations": 4,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 30,
        "value": 3.507441658902,
        "value_label": "3.5074 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.5074 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.625,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 196.191315658426,
          "asset_volatility": 0.21411058977,
          "distance_to_default": 3.507441658902,
          "physical_default_probability": 0.000226218775,
          "risk_neutral_default_probability": 0.000436058087,
          "iterations": 4,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 31,
        "value": 3.46108750991,
        "value_label": "3.4611 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.4611 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.670833333333,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 196.086138343101,
          "asset_volatility": 0.214231762615,
          "distance_to_default": 3.46108750991,
          "physical_default_probability": 0.000268998948,
          "risk_neutral_default_probability": 0.00051889392,
          "iterations": 4,
          "residual": 1e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 32,
        "value": 3.416605781566,
        "value_label": "3.4166 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.4166 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.716666666667,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 195.981031281318,
          "asset_volatility": 0.214353749066,
          "distance_to_default": 3.416605781566,
          "physical_default_probability": 0.000317035123,
          "risk_neutral_default_probability": 0.000611986899,
          "iterations": 4,
          "residual": 2e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 33,
        "value": 3.373871989298,
        "value_label": "3.3739 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.3739 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.7625,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 195.875988044864,
          "asset_volatility": 0.214476592733,
          "distance_to_default": 3.373871989298,
          "physical_default_probability": 0.000370594134,
          "risk_neutral_default_probability": 0.000715870402,
          "iterations": 4,
          "residual": 3e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 34,
        "value": 3.332772794617,
        "value_label": "3.3328 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.3328 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.808333333333,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 195.771002196893,
          "asset_volatility": 0.214600334494,
          "distance_to_default": 3.332772794617,
          "physical_default_probability": 0.000429925648,
          "risk_neutral_default_probability": 0.000831045206,
          "iterations": 4,
          "residual": 5e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 35,
        "value": 3.293204761694,
        "value_label": "3.2932 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.2932 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.854166666667,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 195.666067321869,
          "asset_volatility": 0.214725012385,
          "distance_to_default": 3.293204761694,
          "physical_default_probability": 0.000495261545,
          "risk_neutral_default_probability": 0.000957978091,
          "iterations": 4,
          "residual": 8e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 36,
        "value": 3.255073279351,
        "value_label": "3.2551 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.2551 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.9,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 195.561177052775,
          "asset_volatility": 0.214850661532,
          "distance_to_default": 3.255073279351,
          "physical_default_probability": 0.000566815558,
          "risk_neutral_default_probability": 0.001097100976,
          "iterations": 4,
          "residual": 1.2e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 37,
        "value": 3.21829162302,
        "value_label": "3.2183 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.2183 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.945833333333,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 195.456325095594,
          "asset_volatility": 0.214977314126,
          "distance_to_default": 3.21829162302,
          "physical_default_probability": 0.000644783164,
          "risk_neutral_default_probability": 0.001248810515,
          "iterations": 4,
          "residual": 1.9e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 38,
        "value": 3.182780135629,
        "value_label": "3.1828 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.1828 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.991666666667,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 195.351505251065,
          "asset_volatility": 0.215104999429,
          "distance_to_default": 3.182780135629,
          "physical_default_probability": 0.000729341666,
          "risk_neutral_default_probability": 0.001413468094,
          "iterations": 4,
          "residual": 3e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 39,
        "value": 3.148465509953,
        "value_label": "3.1485 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.1485 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 2.0375,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 195.246711433839,
          "asset_volatility": 0.215233743806,
          "distance_to_default": 3.148465509953,
          "physical_default_probability": 0.000820650452,
          "risk_neutral_default_probability": 0.001591400169,
          "iterations": 4,
          "residual": 4.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 40,
        "value": 3.115280157882,
        "value_label": "3.1153 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.1153 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 2.083333333333,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 195.141937689126,
          "asset_volatility": 0.215363570779,
          "distance_to_default": 3.115280157882,
          "physical_default_probability": 0.000918851387,
          "risk_neutral_default_probability": 0.001782898881,
          "iterations": 4,
          "residual": 6.7e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 41,
        "value": 3.083161654406,
        "value_label": "3.0832 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.0832 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 2.129166666667,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 195.037178206991,
          "asset_volatility": 0.215494501106,
          "distance_to_default": 3.083161654406,
          "physical_default_probability": 0.001024069321,
          "risk_neutral_default_probability": 0.0019882229,
          "iterations": 4,
          "residual": 9.8e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 42,
        "value": 3.052052246039,
        "value_label": "3.0521 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.0521 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 2.175,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 194.932427334338,
          "asset_volatility": 0.21562655287,
          "distance_to_default": 3.052052246039,
          "physical_default_probability": 0.001136412686,
          "risk_neutral_default_probability": 0.002207598459,
          "iterations": 5,
          "residual": 1e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 43,
        "value": 3.021898415154,
        "value_label": "3.0219 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 3.0219 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 2.220833333333,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 194.827679585343,
          "asset_volatility": 0.215759741575,
          "distance_to_default": 3.021898415154,
          "physical_default_probability": 0.001255974158,
          "risk_neutral_default_probability": 0.002441220526,
          "iterations": 5,
          "residual": 2e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 44,
        "value": 2.992650492597,
        "value_label": "2.9927 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 2.9927 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 2.266666666667,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 194.722929649152,
          "asset_volatility": 0.215894080262,
          "distance_to_default": 2.992650492597,
          "physical_default_probability": 0.001382831371,
          "risk_neutral_default_probability": 0.002689254091,
          "iterations": 5,
          "residual": 3e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 45,
        "value": 2.964262312687,
        "value_label": "2.9643 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 2.9643 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 2.3125,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 194.618172396668,
          "asset_volatility": 0.216029579624,
          "distance_to_default": 2.964262312687,
          "physical_default_probability": 0.001517047662,
          "risk_neutral_default_probability": 0.002951835519,
          "iterations": 5,
          "residual": 4e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 46,
        "value": 2.936690905026,
        "value_label": "2.9367 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 2.9367 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 2.358333333333,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 194.513402885446,
          "asset_volatility": 0.216166248121,
          "distance_to_default": 2.936690905026,
          "physical_default_probability": 0.001658672837,
          "risk_neutral_default_probability": 0.003229073971,
          "iterations": 5,
          "residual": 7e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 47,
        "value": 2.90989621864,
        "value_label": "2.9099 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 2.9099 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 2.404166666667,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 194.408616363257,
          "asset_volatility": 0.216304092107,
          "distance_to_default": 2.90989621864,
          "physical_default_probability": 0.001807743946,
          "risk_neutral_default_probability": 0.003521052836,
          "iterations": 5,
          "residual": 9e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 48,
        "value": 2.883840874519,
        "value_label": "2.8838 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 2.8838 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 2.45,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 194.303808270434,
          "asset_volatility": 0.216443115949,
          "distance_to_default": 2.883840874519,
          "physical_default_probability": 0.001964286053,
          "risk_neutral_default_probability": 0.003827831183,
          "iterations": 5,
          "residual": 1.3e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 49,
        "value": 2.858489943149,
        "value_label": "2.8585 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 2.8585 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 2.495833333333,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 194.198974241114,
          "asset_volatility": 0.216583322147,
          "distance_to_default": 2.858489943149,
          "physical_default_probability": 0.002128313006,
          "risk_neutral_default_probability": 0.004149445208,
          "iterations": 5,
          "residual": 1.9e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 50,
        "value": 2.833810744143,
        "value_label": "2.8338 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 2.8338 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 2.541666666667,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 194.094110103516,
          "asset_volatility": 0.216724711457,
          "distance_to_default": 2.833810744143,
          "physical_default_probability": 0.002299828188,
          "risk_neutral_default_probability": 0.004485909659,
          "iterations": 5,
          "residual": 2.6e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 51,
        "value": 2.809772665397,
        "value_label": "2.8098 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 2.8098 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 2.5875,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 193.989211879375,
          "asset_volatility": 0.216867283003,
          "distance_to_default": 2.809772665397,
          "physical_default_probability": 0.00247882524,
          "risk_neutral_default_probability": 0.004837219229,
          "iterations": 5,
          "residual": 3.6e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 52,
        "value": 2.786346999588,
        "value_label": "2.7863 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 2.7863 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 2.633333333333,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 193.884275782637,
          "asset_volatility": 0.217011034395,
          "distance_to_default": 2.786346999588,
          "physical_default_probability": 0.00266528878,
          "risk_neutral_default_probability": 0.005203349922,
          "iterations": 5,
          "residual": 4.8e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 53,
        "value": 2.763506796087,
        "value_label": "2.7635 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 2.7635 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 2.679166666667,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 193.779298217515,
          "asset_volatility": 0.217155961833,
          "distance_to_default": 2.763506796087,
          "physical_default_probability": 0.002859195075,
          "risk_neutral_default_probability": 0.005584260369,
          "iterations": 5,
          "residual": 6.5e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 54,
        "value": 2.741226726589,
        "value_label": "2.7412 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 2.7412 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 2.725,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 193.674275776008,
          "asset_volatility": 0.217302060216,
          "distance_to_default": 2.741226726589,
          "physical_default_probability": 0.0030605127,
          "risk_neutral_default_probability": 0.005979893094,
          "iterations": 5,
          "residual": 8.6e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 55,
        "value": 2.719482962966,
        "value_label": "2.7195 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 2.7195 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 2.770833333333,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 193.569205234693,
          "asset_volatility": 0.217449323244,
          "distance_to_default": 2.719482962966,
          "physical_default_probability": 0.003269203158,
          "risk_neutral_default_probability": 0.006390175738,
          "iterations": 6,
          "residual": 2e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 56,
        "value": 2.698253066262,
        "value_label": "2.6983 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 2.6983 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 2.816666666667,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 193.464083552292,
          "asset_volatility": 0.217597743505,
          "distance_to_default": 2.698253066262,
          "physical_default_probability": 0.003485221477,
          "risk_neutral_default_probability": 0.006815022217,
          "iterations": 6,
          "residual": 3e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 57,
        "value": 2.677515885172,
        "value_label": "2.6775 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 2.6775 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 2.8625,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 193.358907864767,
          "asset_volatility": 0.217747312578,
          "distance_to_default": 2.677515885172,
          "physical_default_probability": 0.003708516769,
          "risk_neutral_default_probability": 0.007254333839,
          "iterations": 6,
          "residual": 5e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 58,
        "value": 2.657251463648,
        "value_label": "2.6573 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 2.6573 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 2.908333333333,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 193.253675482152,
          "asset_volatility": 0.217898021112,
          "distance_to_default": 2.657251463648,
          "physical_default_probability": 0.003939032764,
          "risk_neutral_default_probability": 0.007708000354,
          "iterations": 6,
          "residual": 6e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 59,
        "value": 2.637440956294,
        "value_label": "2.6374 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 2.6374 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 2.954166666667,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 193.148383884238,
          "asset_volatility": 0.218049858911,
          "distance_to_default": 2.637440956294,
          "physical_default_probability": 0.004176708309,
          "risk_neutral_default_probability": 0.008175900954,
          "iterations": 6,
          "residual": 8e-12,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 60,
        "value": 2.618066550926,
        "value_label": "2.6181 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 2.6181 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 3.0,
          "tolerance": 1e-10,
          "max_iterations": 200
        },
        "output": {
          "asset_value": 193.043030716264,
          "asset_volatility": 0.218202815011,
          "distance_to_default": 2.618066550926,
          "physical_default_probability": 0.004421477842,
          "risk_neutral_default_probability": 0.008657905221,
          "iterations": 6,
          "residual": 1.1e-11,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      }
    ]
  },
  {
    "name": "Failure/comparison",
    "description": "Synthetic failure/comparison sweep; only declared fields change while the topic contract remains fixed.",
    "canonical_step": 30,
    "summary": {
      "focus_step": 30,
      "focus_kind": "comparison",
      "canonical_output_match": false,
      "state_counts": {
        "not-converged": 10,
        "converged": 51
      },
      "value_min": 0.0,
      "value_max": 4.431810702244,
      "segments": [
        {
          "start_step": 0,
          "end_step": 9,
          "state": "not-converged",
          "decision": "merton-equity-system-did-not-converge",
          "start_value_label": "diagnostic null",
          "end_value_label": "diagnostic null"
        },
        {
          "start_step": 10,
          "end_step": 60,
          "state": "converged",
          "decision": "merton-equity-system-solved",
          "start_value_label": "4.4318 sigma",
          "end_value_label": "4.4318 sigma"
        }
      ]
    },
    "states": [
      {
        "step": 0,
        "value": 0.0,
        "value_label": "diagnostic null",
        "state": "not-converged",
        "diagnostic": "not-converged: merton-equity-system-did-not-converge",
        "guidance": "Inspect the intermediate components before interpreting diagnostic null; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 1
        },
        "output": {
          "asset_value": null,
          "asset_volatility": null,
          "distance_to_default": null,
          "physical_default_probability": null,
          "risk_neutral_default_probability": null,
          "iterations": 1,
          "residual": 7.43569e-07,
          "state": "not-converged",
          "reason": "merton-equity-system-did-not-converge"
        }
      },
      {
        "step": 1,
        "value": 0.0,
        "value_label": "diagnostic null",
        "state": "not-converged",
        "diagnostic": "not-converged: merton-equity-system-did-not-converge",
        "guidance": "Inspect the intermediate components before interpreting diagnostic null; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 1
        },
        "output": {
          "asset_value": null,
          "asset_volatility": null,
          "distance_to_default": null,
          "physical_default_probability": null,
          "risk_neutral_default_probability": null,
          "iterations": 1,
          "residual": 7.43569e-07,
          "state": "not-converged",
          "reason": "merton-equity-system-did-not-converge"
        }
      },
      {
        "step": 2,
        "value": 0.0,
        "value_label": "diagnostic null",
        "state": "not-converged",
        "diagnostic": "not-converged: merton-equity-system-did-not-converge",
        "guidance": "Inspect the intermediate components before interpreting diagnostic null; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 1
        },
        "output": {
          "asset_value": null,
          "asset_volatility": null,
          "distance_to_default": null,
          "physical_default_probability": null,
          "risk_neutral_default_probability": null,
          "iterations": 1,
          "residual": 7.43569e-07,
          "state": "not-converged",
          "reason": "merton-equity-system-did-not-converge"
        }
      },
      {
        "step": 3,
        "value": 0.0,
        "value_label": "diagnostic null",
        "state": "not-converged",
        "diagnostic": "not-converged: merton-equity-system-did-not-converge",
        "guidance": "Inspect the intermediate components before interpreting diagnostic null; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 1
        },
        "output": {
          "asset_value": null,
          "asset_volatility": null,
          "distance_to_default": null,
          "physical_default_probability": null,
          "risk_neutral_default_probability": null,
          "iterations": 1,
          "residual": 7.43569e-07,
          "state": "not-converged",
          "reason": "merton-equity-system-did-not-converge"
        }
      },
      {
        "step": 4,
        "value": 0.0,
        "value_label": "diagnostic null",
        "state": "not-converged",
        "diagnostic": "not-converged: merton-equity-system-did-not-converge",
        "guidance": "Inspect the intermediate components before interpreting diagnostic null; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 2
        },
        "output": {
          "asset_value": null,
          "asset_volatility": null,
          "distance_to_default": null,
          "physical_default_probability": null,
          "risk_neutral_default_probability": null,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "not-converged",
          "reason": "merton-equity-system-did-not-converge"
        }
      },
      {
        "step": 5,
        "value": 0.0,
        "value_label": "diagnostic null",
        "state": "not-converged",
        "diagnostic": "not-converged: merton-equity-system-did-not-converge",
        "guidance": "Inspect the intermediate components before interpreting diagnostic null; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 2
        },
        "output": {
          "asset_value": null,
          "asset_volatility": null,
          "distance_to_default": null,
          "physical_default_probability": null,
          "risk_neutral_default_probability": null,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "not-converged",
          "reason": "merton-equity-system-did-not-converge"
        }
      },
      {
        "step": 6,
        "value": 0.0,
        "value_label": "diagnostic null",
        "state": "not-converged",
        "diagnostic": "not-converged: merton-equity-system-did-not-converge",
        "guidance": "Inspect the intermediate components before interpreting diagnostic null; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 2
        },
        "output": {
          "asset_value": null,
          "asset_volatility": null,
          "distance_to_default": null,
          "physical_default_probability": null,
          "risk_neutral_default_probability": null,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "not-converged",
          "reason": "merton-equity-system-did-not-converge"
        }
      },
      {
        "step": 7,
        "value": 0.0,
        "value_label": "diagnostic null",
        "state": "not-converged",
        "diagnostic": "not-converged: merton-equity-system-did-not-converge",
        "guidance": "Inspect the intermediate components before interpreting diagnostic null; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 2
        },
        "output": {
          "asset_value": null,
          "asset_volatility": null,
          "distance_to_default": null,
          "physical_default_probability": null,
          "risk_neutral_default_probability": null,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "not-converged",
          "reason": "merton-equity-system-did-not-converge"
        }
      },
      {
        "step": 8,
        "value": 0.0,
        "value_label": "diagnostic null",
        "state": "not-converged",
        "diagnostic": "not-converged: merton-equity-system-did-not-converge",
        "guidance": "Inspect the intermediate components before interpreting diagnostic null; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 2
        },
        "output": {
          "asset_value": null,
          "asset_volatility": null,
          "distance_to_default": null,
          "physical_default_probability": null,
          "risk_neutral_default_probability": null,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "not-converged",
          "reason": "merton-equity-system-did-not-converge"
        }
      },
      {
        "step": 9,
        "value": 0.0,
        "value_label": "diagnostic null",
        "state": "not-converged",
        "diagnostic": "not-converged: merton-equity-system-did-not-converge",
        "guidance": "Inspect the intermediate components before interpreting diagnostic null; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 2
        },
        "output": {
          "asset_value": null,
          "asset_volatility": null,
          "distance_to_default": null,
          "physical_default_probability": null,
          "risk_neutral_default_probability": null,
          "iterations": 2,
          "residual": 5.5e-11,
          "state": "not-converged",
          "reason": "merton-equity-system-did-not-converge"
        }
      },
      {
        "step": 10,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 3
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 11,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 3
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 12,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 3
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 13,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 3
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 14,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 3
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 15,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 3
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 16,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 3
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 17,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 4
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 18,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 4
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 19,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 4
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 20,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 4
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 21,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 4
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 22,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 4
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 23,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 4
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 24,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 5
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 25,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 5
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 26,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 5
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 27,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 5
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 28,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 5
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 29,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 5
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 30,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 5
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 31,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 6
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 32,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 6
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 33,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 6
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 34,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 6
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 35,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 6
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 36,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 6
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 37,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 7
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 38,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 7
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 39,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 7
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 40,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 7
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 41,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 7
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 42,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 7
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 43,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 7
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 44,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 8
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 45,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 8
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 46,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 8
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 47,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 8
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 48,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 8
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 49,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 8
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 50,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 9
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 51,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 9
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 52,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 9
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 53,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 9
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 54,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 9
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 55,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 9
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 56,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 9
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 57,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 10
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 58,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 10
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 59,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 10
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      },
      {
        "step": 60,
        "value": 4.431810702244,
        "value_label": "4.4318 sigma",
        "state": "converged",
        "diagnostic": "converged: merton-equity-system-solved",
        "guidance": "Inspect the intermediate components before interpreting 4.4318 sigma; definition, horizon, clocks, and calibration remain part of the output.",
        "input": {
          "equity_value": 120.0,
          "equity_volatility": 0.35,
          "debt_face_value": 80.0,
          "risk_free_rate": 0.03,
          "asset_drift": 0.06,
          "horizon_years": 1.0,
          "tolerance": 0.0,
          "max_iterations": 10
        },
        "output": {
          "asset_value": 197.635612721046,
          "asset_volatility": 0.212513018382,
          "distance_to_default": 4.431810702244,
          "physical_default_probability": 4.672252e-06,
          "risk_neutral_default_probability": 8.907831e-06,
          "iterations": 3,
          "residual": 0.0,
          "state": "converged",
          "reason": "merton-equity-system-solved"
        }
      }
    ]
  }
]