Build a transparent runway sensitivity that preserves the monthly cash-flow path and labels nonburning, short-window, and negative-liquidity states.
The decision this tutorial makes visible
Early-stage firms can have intentionally negative earnings, so survival capacity and financing timing often matter more than mature-company margins.
The precise question is: How can current liquidity, historical cash burn, burn trend, obligations, and revenue cover be converted into a review score without pretending to forecast financing?
A practitioner needs to know what the diagnostic does and does not justify. A builder needs a contract that can be reproduced from the same point-in-time inputs in Python, TypeScript, a visual, and a browser lab.
Intuition before notation
Runway is a fuel-gauge sensitivity: it says how long today's declared resources could cover a historical burn rate, not what management will actually spend or raise.
The result depends on the declared algorithm scope, input clocks, units, equality and rounding policies, and unsupported-state treatment. Change one of those and the output represents a different decision even when its field name is unchanged.
Scope and nearby methods
This contract uses at least six historical monthly net cash flows and matching revenue observations. It treats committed liquidity conservatively, subtracts obligations and a minimum cash reserve, and does not assume future financing.
| Variant | Definition | Best use | Main limitation |
|---|---|---|---|
| Selected historical-burn sensitivity | Current resources divided by observed burn | Transparent monitoring | Not a management forecast |
| Forward operating plan | Scenario-based cash forecast | Board and treasury planning | Usually private and uncertain |
| Going-concern assessment | Accounting conclusion and disclosures | Financial reporting | A runway score cannot replace it |
What is sourced, selected, synthetic, and derived
| Role | Material claim | Evidence | Boundary |
|---|---|---|---|
| sourced caution | Liquidity disclosure considers cash requirements, commitments, uncertainties, and capital resources. | SEC FRM Topic 9 | It does not prescribe this score. |
| sourced caution | A disclosed cash-burn metric needs a clear definition and management-use context. | SEC guidance | Historical burn is not a forecast. |
| package choice | The six-month window, bands, weights, and 12-month state are teaching choices. | Repository contract | They are not a going-concern conclusion. |
| derived output | Runway comes from declared current resources and observed synthetic flows. | Calculation ledger | It assumes no future financing or spending change. |
The authoritative sources support only the exact facts named in the claim ledger. They do not certify the synthetic numbers in this tutorial. The repository fixture is deliberately invented for auditability, and the displayed output is author-derived under the selected implementation choice.
Formula, symbols, and numerical policy
available = cash + liquid investments + unconditional facility − obligations − minimum cash; runway = available / average six-month burn when burn > 0.
| Symbol | Meaning | Unit | Policy |
|---|---|---|---|
| L | available liquidity | currency | Exclude conditional or restricted resources |
| b | six-month average burn magnitude | currency/month | Zero when average flow is nonnegative |
| R | runway | months | L/b only when b>0 |
- Use IEEE-754 binary64 arithmetic without intermediate rounding.
- Treat percentages as decimal fractions and label percentage-point changes explicitly.
- Clamp only declared component transforms to [0,100]; never clamp raw regulatory or accounting inputs silently.
- Round only for presentation after the full component, penalty, and coverage ledger is stored.
Read the formula in the same order as the algorithm. Validate identity, ordering, units, and supported state first. Apply the selected equality and window rules second. Calculate with unrounded numeric values. Round only at the declared presentation boundary, and preserve null as a diagnostic rather than coercing it to zero.
Build the algorithm
- Freeze the knowledge cutoff and classify unrestricted, liquid, committed, conditional, and restricted resources.
- Subtract near-term obligations and the operating-cash reserve.
- Calculate six-month burn and the two three-month burn windows.
- Compute runway only when burn is positive, then score all four dimensions.
- Publish the path, assumptions, state, and sensitivity—not only a months figure.
Production-minded operational checklist
- Resolve sector and framework before calculating.
- Freeze scoring and knowledge-cutoff timestamps.
- Reconcile each input to its filing, regulator, provider, and reporting perimeter.
- Inspect component scores, penalties, and coverage before the headline.
- Retain abstention and unsupported-scope reasons for the integrated router.
The checklist is intentionally strict: an explicit rejection is safer than a plausible output built from stale, malformed, or unsupported state.
Worked synthetic example
The canonical fixture is synthetic teaching data, not an observed control
event, customer order, or broker execution. Its primary author-derived output,
runway_score, is 79.0. The complete input and output
are in datasets/canonical-input.json and datasets/expected-output.json.
The fixture has 56 of available liquidity after obligations and reserve. Its burn improves across the two three-month windows, so the lab reveals both the runway arithmetic and the improving burn trend.
Counterfactual checkpoint
Accelerate recent burn. Hold liquidity fixed and make the latest three cash-flow months more negative. The output changes because Monthly burn rises, runway shortens, and the burn-trend component weakens together.
The structured result retains state and diagnostics in addition to the primary number. That makes the calculation independently reviewable and prevents a partial, null, rejected, or venue-bounded outcome from being mistaken for an unqualified value.
Boundary and counterexample workbook
The playground computes every scenario at 61 deterministic parameter states.
The table uses the declared focus step and states whether that focus reproduces
the canonical fixture. The full state ledger and compressed transition
segments are in datasets/scenario-results.json.
| Scenario | Review focus | Purpose | State | Primary output | Diagnostic | Decision segments |
|---|---|---|---|---|---|---|
| Canonical driver sweep | Step 30 · canonical fixture | Move one primary causal driver through the canonical midpoint. | strong-review-band | runway score 79.0 | strong-review-band · historical-burn-sensitivity-not-management-forecast | 3 |
| Adverse operating stress | Step 30 · comparison focus | Apply a controlled operating or earnings stress while retaining the framework. | strong-review-band | runway score 75.1 | strong-review-band · historical-burn-sensitivity-not-management-forecast | 3 |
| Balance-sheet resilience | Step 30 · comparison focus | Vary a funding, leverage, capital, or liquidity channel. | strong-review-band | runway score 84.2 | strong-review-band · historical-burn-sensitivity-not-management-forecast | 2 |
| Boundary crossing | Step 30 · comparison focus | Cross a declared review boundary and inspect equality behavior. | mixed-review-band | runway score 71.0 | mixed-review-band · historical-burn-sensitivity-not-management-forecast | 3 |
| Evidence-quality stress | Step 30 · comparison focus | Change evidence usability or freshness without hiding the diagnostic. | strong-review-band | runway score 75.5 | strong-review-band · historical-burn-sensitivity-not-management-forecast | 2 |
| Concentration or mix | Step 30 · canonical fixture | Vary concentration, mix, or component balance. | strong-review-band | runway score 79.0 | strong-review-band · historical-burn-sensitivity-not-management-forecast | 2 |
| Recovery path | Step 30 · comparison focus | Trace a recovery from an adverse state toward a resilient state. | strong-review-band | runway score 82.6 | strong-review-band · historical-burn-sensitivity-not-management-forecast | 2 |
These rows are not backtest observations. They are controlled counterexamples that expose how one driver changes the state, output, or reason code while the rest of the contract stays fixed.
Visualize the boundary
Open this SVG at full size, or use the guided playground to compare the seven topic-specific canonical, boundary, policy, and failure scenarios.
The Mermaid flow answers where the selected calculation sits in the processing sequence. The SVG keeps the formula, output, decision boundary, and invariant visible together. The lab lets the reader step through the same structured states without changing the underlying definition.
Implementation walkthrough
The Python and TypeScript references begin with the same validation contract, reject malformed and unsupported state before calculation, preserve declared ordering and rounding policies, and return structured diagnostics rather than one context-free number.
The main implementation branches are:
- Available liquidity is negative — Emit negative-available-liquidity, because Declared near-term resources do not cover obligations plus reserve.
- Average burn is zero — Emit nonburning-observation and null runway, because Division would create false infinity.
- Runway is below 12 months — Emit funding-window-under-12-months, because The package calls for explicit funding-window review.
Neither reference silently fetches data, mutates caller-owned inputs outside the declared engine behavior, guesses hidden state, or substitutes a provider default. Shared JSON fixtures make value, null, state, and reason-code drift visible across languages.
Testing and validation
Definition tests compare every canonical field, reject malformed state, and exercise the material boundary. Family validation recomputes every playground state from the reference function. Independent arithmetic is recorded beside the fixture rather than inferred only from implementation output.
The audit must preserve these invariants:
- framework and policy version
- point-in-time normalized input ledger
- component transform thresholds and scores
- weight vector and penalties
- coverage, state, reason, and final output
Passing the suite proves the selected package contract and Python/TypeScript parity; it does not prove empirical usefulness for a live issuer universe.
Failure modes and misuse
- The 0-100 teaching bands and default weights are package choices, not regulations, ratings, or market standards.
- Definition fidelity and code parity do not establish predictive validity, calibration, causality, fair value, or investment performance.
- Accounting frameworks, prudential regimes, business mixes, and reporting perimeters can make apparently identical ratios incomparable.
- A complete component ledger can still omit material qualitative, governance, legal, catastrophe, operational, or market risks.
Debugging order
When a result looks surprising, inspect the state in this order:
- Confirm framework and reporting perimeter
- Check units and knowledge dates
- Recalculate raw intermediates
- Inspect bounded component transforms
- Reconcile weights, penalties, coverage, and state
Evidence and historical boundary
Historical decision: not useful. A named Early-Stage Liquidity and Runway Score case would introduce issuer identity, filing and regulator scope, restatement, data-license, and scoring-policy questions without teaching the deterministic mechanism better than a controlled synthetic record.
The primary sources are SEC FRM Topic 9, SEC liquidity metric guidance, FASB ASU 2014-15. They support the source roles listed in the research ledger, not a redistributable historical observation, a private participant decision, production conformance certification, execution-quality result, profitability claim, or prediction claim.
Summary and next topic
You can now compute and audit Early-Stage Liquidity and Runway Score before passing its versioned output to the integrated scoring router. The learning flow is: Utility Fundamental Score → Early-Stage Liquidity and Runway Score → Cyclical and Commodity-Cycle Normalization. Carry the result forward only with its scope, clock, state, and evidence label.
Verified model contract — Level 1
- Selected calculation:
available = cash + liquid investments + unconditional facility − obligations − minimum cash; runway = available / average six-month burn when burn > 0. - Reproducibility boundary: the canonical fixture is synthetic; the stored input, intermediate ledger, output, and cross-language implementations define the executable example.
- Interpretation ceiling: Definition fidelity and code parity do not establish predictive validity, calibration, causality, fair value, or investment performance.
Level 2 learning layer
How to choose this model or a nearby method
| Method | Best use | Assumption that must hold | Main limitation |
|---|---|---|---|
| Selected historical-burn sensitivity | Transparent monitoring | Past six months are informative | Not a management forecast |
| Forward operating plan | Board and treasury planning | Forecast assumptions are governed | Usually private and uncertain |
| Going-concern assessment | Financial reporting | Full standard and management evidence | A runway score cannot replace it |
The selected package is appropriate only when its framework tag, reporting perimeter, unit policy, and point-in-time evidence contract are all satisfied. If a stop condition in the topic decision matrix fires, use the named review, reroute, or abstention state instead of forcing a score.
Compact glossary
| Symbol | Meaning | Unit | Policy |
|---|---|---|---|
L | available liquidity | currency | Exclude conditional or restricted resources |
b | six-month average burn magnitude | currency/month | Zero when average flow is nonnegative |
R | runway | months | L/b only when b>0 |
Visual asset map
| Asset | Learning job | Status |
|---|---|---|
| Article hero | See route → normalize → calculate → decide at a glance | Ready |
| System map | Connect formula, boundary, invariant, counterfactual, and output | Ready |
| Model anatomy | Follow the four-stage calculation pipeline | Ready |
| Component ledger | Reconstruct the headline from named dimensions | Ready |
| Decision boundary | Separate a computable result from a permissible interpretation | Ready |
| Evidence clock | Prevent point-in-time leakage | Ready |
| Mermaid flow | Inspect the text-native algorithm flow | Ready |
| Guided playground | Predict, reveal, sweep 427 calculations, and explain state changes | Ready |
Related concepts and continuation
- Previous family topic: D18-F10-A04
- Next family topic: D18-F10-A06
- Weight governance: D18-F10-A08
- Coverage and abstention: D18-F10-A09
Deep visual atlas
The teaching sequence is route → normalize → calculate → decide. Use the component ledger to reconstruct the headline, the boundary map to stop unsupported interpretation, and the evidence clock to block hindsight.
Guided playground protocol
- Orient: identify the framework, active driver, and invariant.
- Predict: commit to decrease, stay flat, or increase before revealing the adjacent numeric result.
- Experiment: sweep all 61 computed states in each of seven scenarios and inspect discontinuities.
- Explain: reconcile
available liquidity, six-month burn, and three-month burn ratioto the headline and apply this boundary: Conditional financing, forecast cash flows, or a mismatched observation clock require exclusion or a new model.
Rendered from the canonical Mermaid sources linked by this article.
Early-Stage Liquidity and Runway Score calculation flow
This flow identifies the selected calculation stages and the structured output.
Takeaway: A useful runway result shows the cash path and assumptions behind the months figure.
ReferencesPrimary sources and evidence notesExpand the source trail, evidence role, and limitations behind the engineering choices.
Expand the source trail, evidence role, and limitations behind the engineering choices.
S1 — Financial Reporting Manual — Management's Discussion and Analysis
- Organization or authors: U.S. Securities and Exchange Commission
- Source type: Official staff manual
- Publication or effective date: Updated through 2020; accessed 2026-08-08
- Version: Topic 9
- URL or DOI: https://www.sec.gov/about/divisions-offices/division-corporation-finance/financial-reporting-manual/frm-topic-9
- Accessed: 2026-08-09
- Jurisdiction: United States SEC reporting
- Supports: Liquidity analysis addresses cash generation, cash requirements, commitments, uncertainties, and capital resources.
- Limitations: The manual does not prescribe a runway score or forecast future financing.
S2 — Disclosure considerations regarding operations, liquidity, and capital resources
- Organization or authors: U.S. Securities and Exchange Commission, Division of Corporation Finance
- Source type: Official staff guidance
- Publication or effective date: June 2020; accessed 2026-08-08
- Version: CF Disclosure Guidance Topic 9A
- URL or DOI: https://www.sec.gov/rules-regulations/staff-guidance/disclosure-guidance/coronavirus-covid-19-disclosure-considerations
- Accessed: 2026-08-09
- Jurisdiction: United States SEC reporting
- Supports: When cash-burn or daily-cash-use metrics are disclosed, their definitions and management use should be explained.
- Limitations: Does not endorse the package's historical-burn sensitivity as a management forecast.
S3 — Presentation of Financial Statements—Going Concern
- Organization or authors: Financial Accounting Standards Board
- Source type: Official accounting update
- Publication or effective date: Issued 2014; accessed 2026-08-08
- Version: ASC 205-40 update
- URL or DOI: https://fasb.org/page/document?pdf=ASU+2014-15.pdf
- Accessed: 2026-08-09
- Jurisdiction: U.S. GAAP
- Supports: Management evaluates substantial doubt and related disclosures under the accounting standard.
- Limitations: A repository runway score is not a going-concern conclusion.
Evidence boundary
Sources define sector measures, disclosure regimes, and methodological cautions. They do not endorse the repository's synthetic fixtures, weights, score bands, or investment use.
Full dependency-light reference implementations in both supported languages.
/** Deterministic TypeScript reference for D18-F10 sector-specific scoring. */
export type RecordValue = Record<string, any>;
const numberValue = (data: RecordValue, name: string): number => {
const value = data[name];
if (typeof value !== "number" || !Number.isFinite(value)) throw new TypeError(`${name} must be a finite number`);
return value;
};
const nonnegative = (data: RecordValue, name: string): number => {
const value = numberValue(data, name); if (value < 0) throw new RangeError(`${name} must be nonnegative`); return value;
};
const positive = (data: RecordValue, name: string): number => {
const value = numberValue(data, name); if (value <= 0) throw new RangeError(`${name} must be positive`); return value;
};
const textValue = (data: RecordValue, name: string): string => {
const value = data[name]; if (typeof value !== "string" || !value.trim()) throw new TypeError(`${name} must be a nonempty string`); return value.trim();
};
const dateValue = (value: unknown, name: string): Date => {
if (typeof value !== "string" || !/^\d{4}-\d{2}-\d{2}$/.test(value)) throw new TypeError(`${name} must be YYYY-MM-DD`);
const result = new Date(`${value}T00:00:00Z`); if (!Number.isFinite(result.getTime()) || result.toISOString().slice(0, 10) !== value) throw new RangeError(`${name} must be YYYY-MM-DD`); return result;
};
const requireFramework = (data: RecordValue, expected: string): void => { if (textValue(data, "framework") !== expected) throw new RangeError(`framework must be ${expected}`); };
const clamp = (value: number, low = 0, high = 100): number => Math.min(high, Math.max(low, value));
const higher = (value: number, weak: number, strong: number): number => { if (strong <= weak) throw new RangeError("strong threshold must exceed weak threshold"); return clamp(100 * (value - weak) / (strong - weak)); };
const lower = (value: number, strong: number, weak: number): number => { if (weak <= strong) throw new RangeError("weak threshold must exceed strong threshold"); return clamp(100 * (weak - value) / (weak - strong)); };
const centered = (value: number, center: number, fullDistance: number, zeroDistance: number): number => {
if (zeroDistance <= fullDistance) throw new RangeError("zero-score distance must exceed full-score distance");
return clamp(100 * (zeroDistance - Math.abs(value - center)) / (zeroDistance - fullDistance));
};
const weightsFor = (data: RecordValue, names: string[]): Record<string, number> => {
const raw = data.weights;
if (!raw || typeof raw !== "object" || Array.isArray(raw) || Object.keys(raw).sort().join("|") !== [...names].sort().join("|")) throw new RangeError("weights must contain exactly the declared component names");
const result = Object.fromEntries(names.map(name => [name, nonnegative(raw, name)]));
const total = Object.values(result).reduce((sum, value) => sum + value, 0);
if (Math.abs(total - 1) > 1e-9) throw new RangeError("weights must sum to 1");
return result;
};
const weightedScore = (components: Record<string, number>, weights: Record<string, number>): number => Object.entries(components).reduce((sum, [name, value]) => sum + value * weights[name], 0);
const scoreState = (score: number): string => score >= 75 ? "strong-review-band" : score >= 50 ? "mixed-review-band" : "weak-review-band";
function bankScore(data: RecordValue): RecordValue {
requireFramework(data, "basel-iii-teaching-v1");
const names = ["capital", "leverage", "short_liquidity", "stable_funding", "asset_quality", "coverage", "margin", "efficiency"];
const weights = weightsFor(data, names);
const values = {cet1_ratio: nonnegative(data,"cet1_ratio"), leverage_ratio: nonnegative(data,"leverage_ratio"), lcr: nonnegative(data,"lcr"), nsfr: nonnegative(data,"nsfr"), npl_ratio: nonnegative(data,"npl_ratio"), provision_coverage_ratio: nonnegative(data,"provision_coverage_ratio"), net_interest_margin: numberValue(data,"net_interest_margin"), cost_income_ratio: nonnegative(data,"cost_income_ratio")};
const components = {capital:higher(values.cet1_ratio,.07,.14), leverage:higher(values.leverage_ratio,.03,.06), short_liquidity:higher(values.lcr,1,1.4), stable_funding:higher(values.nsfr,1,1.3), asset_quality:lower(values.npl_ratio,.02,.08), coverage:higher(values.provision_coverage_ratio,.6,1.2), margin:higher(values.net_interest_margin,.01,.04), efficiency:lower(values.cost_income_ratio,.4,.7)};
const minimums = data.minimums; if (!minimums || typeof minimums !== "object" || Array.isArray(minimums)) throw new TypeError("minimums must be an object");
const checks: Record<string,number> = {cet1_ratio:nonnegative(minimums,"cet1_ratio"), leverage_ratio:nonnegative(minimums,"leverage_ratio"), lcr:nonnegative(minimums,"lcr"), nsfr:nonnegative(minimums,"nsfr")};
const breaches = Object.entries(checks).filter(([name, minimum]) => values[name as keyof typeof values] < minimum).map(([name])=>name);
const base = weightedScore(components, weights), penalty = 12.5 * breaches.length, score = clamp(base - penalty);
return {state:breaches.length?"prudential-floor-review":scoreState(score),method:"bank-sector-score-v1",component_scores:components,weights,base_score:base,floor_breaches:breaches,penalty,fundamental_score:score,coverage_ratio:1,reason:"package-bands-with-declared-prudential-minimums"};
}
function insuranceScore(data: RecordValue): RecordValue {
requireFramework(data,"solvency-ii-nonlife-teaching-v1");
const names=["solvency","minimum_capital","underwriting","reserve_quality","own_fund_quality","concentration","profitability"], weights=weightsFor(data,names);
const values={scr_coverage_ratio:nonnegative(data,"scr_coverage_ratio"),mcr_coverage_ratio:nonnegative(data,"mcr_coverage_ratio"),combined_ratio:nonnegative(data,"combined_ratio"),adverse_reserve_development_ratio:numberValue(data,"adverse_reserve_development_ratio"),tier1_own_funds_share:nonnegative(data,"tier1_own_funds_share"),investment_concentration_ratio:nonnegative(data,"investment_concentration_ratio"),return_on_equity:numberValue(data,"return_on_equity")};
const components={solvency:higher(values.scr_coverage_ratio,1,2),minimum_capital:higher(values.mcr_coverage_ratio,1,3),underwriting:lower(values.combined_ratio,.88,1.08),reserve_quality:lower(values.adverse_reserve_development_ratio,-.02,.08),own_fund_quality:higher(values.tier1_own_funds_share,.5,.9),concentration:lower(values.investment_concentration_ratio,.1,.4),profitability:higher(values.return_on_equity,.02,.15)};
const breaches=["scr_coverage_ratio","mcr_coverage_ratio"].filter(name=>values[name as keyof typeof values]<1),base=weightedScore(components,weights),penalty=20*breaches.length,score=clamp(base-penalty);
return {state:breaches.length?"capital-requirement-review":scoreState(score),method:"insurance-sector-score-v1",component_scores:components,weights,base_score:base,floor_breaches:breaches,penalty,fundamental_score:score,coverage_ratio:1,reason:"solvency-ii-tagged-nonlife-package-bands"};
}
function reitScore(data: RecordValue): RecordValue {
requireFramework(data,"nareit-equity-reit-teaching-v1");
const names=["distribution","leverage","coverage","occupancy","same_store_growth","liquidity"],weights=weightsFor(data,names);
const ffo=numberValue(data,"nareit_ffo"),capex=nonnegative(data,"recurring_capex"),rent=numberValue(data,"straight_line_rent_adjustment"),dividends=positive(data,"common_dividends"),ebitda=positive(data,"ebitda_re"),interest=positive(data,"interest_expense"),nearDebt=positive(data,"near_term_debt_maturities");
const affo=ffo-capex-rent,distribution=affo/dividends,leverage=nonnegative(data,"net_debt")/ebitda,interestCoverage=ebitda/interest,liquidity=nonnegative(data,"available_liquidity")/nearDebt;
const components={distribution:higher(distribution,.8,1.4),leverage:lower(leverage,3.5,8),coverage:higher(interestCoverage,1.5,5),occupancy:higher(nonnegative(data,"occupancy_ratio"),.8,.97),same_store_growth:higher(numberValue(data,"same_store_noi_growth"),-.05,.08),liquidity:higher(liquidity,.75,2)};
const score=weightedScore(components,weights);
return {state:affo<=0?"affo-proxy-deficit-review":scoreState(score),method:"reit-sector-score-v1",nareit_ffo:ffo,affo_proxy:affo,distribution_coverage:distribution,net_debt_to_ebitda_re:leverage,interest_coverage:interestCoverage,liquidity_coverage:liquidity,component_scores:components,weights,fundamental_score:score,coverage_ratio:1,reason:"nareit-ffo-plus-explicit-package-affo-proxy"};
}
function utilityScore(data: RecordValue): RecordValue {
requireFramework(data,"ferc-regulated-electric-teaching-v1");
const names=["earned_return","cash_debt","capital_structure","interest_coverage","capex_funding","regulatory_lag","rate_base_growth"],weights=weightsFor(data,names);
const allowed=positive(data,"allowed_roe"),earned=numberValue(data,"earned_roe"),debt=positive(data,"total_debt"),ffoDebt=numberValue(data,"funds_from_operations")/debt,interestCoverage=numberValue(data,"ebit")/positive(data,"interest_expense"),capexFunding=numberValue(data,"cash_from_operations")/positive(data,"capital_expenditure");
const components={earned_return:centered(earned-allowed,0,.005,.04),cash_debt:higher(ffoDebt,.08,.22),capital_structure:lower(nonnegative(data,"debt_to_capital"),.4,.65),interest_coverage:higher(interestCoverage,1.5,5),capex_funding:higher(capexFunding,.4,1),regulatory_lag:lower(nonnegative(data,"regulatory_lag_months"),3,18),rate_base_growth:centered(numberValue(data,"rate_base_growth"),.05,.01,.08)};
const score=weightedScore(components,weights);
return {state:scoreState(score),method:"utility-sector-score-v1",earned_allowed_roe_gap:earned-allowed,ffo_to_debt:ffoDebt,interest_coverage:interestCoverage,capex_funding_ratio:capexFunding,component_scores:components,weights,fundamental_score:score,coverage_ratio:1,reason:"ferc-tagged-package-bands"};
}
function earlyStageScore(data: RecordValue): RecordValue {
requireFramework(data,"early-stage-liquidity-teaching-v1");
const names=["runway","burn_trend","obligation_cover","revenue_cover"],weights=weightsFor(data,names),cashFlows=data.monthly_net_cash_flows,revenues=data.monthly_revenue;
if(!Array.isArray(cashFlows)||cashFlows.length<6)throw new RangeError("monthly_net_cash_flows must contain at least 6 observations");
if(!Array.isArray(revenues)||revenues.length!==cashFlows.length)throw new RangeError("monthly_revenue must match cash-flow history");
const flows=cashFlows.map((v:any)=>numberValue({v},"v")),revs=revenues.map((v:any)=>nonnegative({v},"v"));
const unrestricted=nonnegative(data,"unrestricted_cash"),investments=nonnegative(data,"liquid_investments"),facility=nonnegative(data,"unconditionally_committed_facility"),obligations=nonnegative(data,"near_term_obligations"),minimumCash=nonnegative(data,"minimum_operating_cash");
const available=unrestricted+investments+facility-obligations-minimumCash,latest=flows.slice(-6),burn=Math.max(0,-latest.reduce((a:number,b:number)=>a+b,0)/latest.length),prior=Math.max(0,-latest.slice(0,3).reduce((a:number,b:number)=>a+b,0)/3),current=Math.max(0,-latest.slice(3).reduce((a:number,b:number)=>a+b,0)/3),burnRatio=prior>0?current/prior:(current===0?0:2),gross=unrestricted+investments+facility,obligationCover=obligations>0?gross/obligations:10,latestRevenue=revs.slice(-3).reduce((a:number,b:number)=>a+b,0)/3,revenueCover=current>0?latestRevenue/current:10,runway=burn>0?available/burn:null;
const components={runway:runway===null?100:higher(runway,6,24),burn_trend:lower(burnRatio,.75,1.25),obligation_cover:higher(obligationCover,.75,2),revenue_cover:higher(revenueCover,0,1)},score=weightedScore(components,weights);
const state=available<0?"negative-available-liquidity":runway===null?"nonburning-observation":runway<12?"funding-window-under-12-months":scoreState(score);
return {state,method:"early-stage-runway-score-v1",available_liquidity:available,monthly_burn:burn,prior_three_month_burn:prior,latest_three_month_burn:current,burn_ratio:burnRatio,runway_months:runway,obligation_coverage:obligationCover,revenue_to_burn:revenueCover,component_scores:components,weights,runway_score:score,coverage_ratio:1,reason:"historical-burn-sensitivity-not-management-forecast"};
}
const medianValue=(values:number[]):number=>{const sorted=[...values].sort((a,b)=>a-b),middle=Math.floor(sorted.length/2);return sorted.length%2?sorted[middle]:(sorted[middle-1]+sorted[middle])/2;};
function cyclicalScore(data:RecordValue):RecordValue{
requireFramework(data,"cyclical-midcycle-teaching-v1");
const names=["normalized_margin","normalized_leverage","cash_consistency","cycle_balance"],weights=weightsFor(data,names),arrays:Record<string,number[]>={};
for(const name of ["realized_price_history","unit_cost_history","volume_history","free_cash_flow_history"]){const raw=data[name];if(!Array.isArray(raw)||raw.length<7)throw new RangeError(`${name} must contain at least 7 observations`);arrays[name]=raw.map((v:any)=>numberValue({v},"v"));}
if(new Set(Object.values(arrays).map(v=>v.length)).size!==1)throw new RangeError("cycle histories must have equal length");
const prices=arrays.realized_price_history,costs=arrays.unit_cost_history,volumes=arrays.volume_history;if([...prices,...costs,...volumes].some(v=>v<=0))throw new RangeError("price, cost, and volume histories must be positive");
const normalizedPrice=medianValue(prices),normalizedCost=medianValue(costs),normalizedVolume=medianValue(volumes),revenue=normalizedPrice*normalizedVolume,ebitda=(normalizedPrice-normalizedCost)*normalizedVolume-nonnegative(data,"fixed_costs"),margin=ebitda/revenue,netDebt=nonnegative(data,"net_debt"),leverage=ebitda>0?netDebt/ebitda:null,positiveFcf=arrays.free_cash_flow_history.filter(v=>v>0).length/arrays.free_cash_flow_history.length,currentPrice=positive(data,"current_realized_price"),percentile=prices.filter(v=>v<=currentPrice).length/prices.length;
const components={normalized_margin:higher(margin,0,.3),normalized_leverage:leverage===null?0:lower(leverage,.5,4),cash_consistency:higher(positiveFcf,.3,.9),cycle_balance:centered(percentile,.5,.1,.5)},score=weightedScore(components,weights);
return {state:ebitda<=0?"nonpositive-midcycle-ebitda-review":scoreState(score),method:"cyclical-midcycle-normalization-v1",normalized_price:normalizedPrice,normalized_unit_cost:normalizedCost,normalized_volume:normalizedVolume,normalized_revenue:revenue,normalized_ebitda:ebitda,normalized_margin:margin,normalized_net_leverage:leverage,positive_fcf_ratio:positiveFcf,cycle_percentile:percentile,component_scores:components,weights,normalized_score:score,coverage_ratio:1,reason:"point-in-time-median-cycle-window"};
}
function holdingCompanyScore(data:RecordValue):RecordValue{
requireFramework(data,"holding-company-lookthrough-teaching-v1");
const names=["nav_buffer","lookthrough_leverage","parent_coverage","diversification","freshness","listed_coverage"],weights=weightsFor(data,names),holdings=data.holdings;
if(!Array.isArray(holdings)||holdings.length<2)throw new RangeError("holdings must contain at least two records");
const ids=new Set<string>(),rows=holdings.map((raw:any)=>{if(!raw||typeof raw!=="object"||Array.isArray(raw))throw new TypeError("each holding must be an object");const id=textValue(raw,"id");if(ids.has(id))throw new RangeError("holding IDs must be unique");ids.add(id);const ownership=numberValue(raw,"ownership_ratio");if(!(ownership>0&&ownership<=1))throw new RangeError("ownership_ratio must be in (0, 1]");if(typeof raw.listed!=="boolean"||typeof raw.stale!=="boolean")throw new TypeError("listed and stale must be booleans");return{id,ownership_ratio:ownership,attributable_equity_value:ownership*nonnegative(raw,"equity_value"),attributable_debt:ownership*nonnegative(raw,"debt"),attributable_dividends:ownership*nonnegative(raw,"dividends_to_parent"),listed:raw.listed,stale:raw.stale};});
const parentCash=nonnegative(data,"parent_cash"),parentDebt=nonnegative(data,"parent_debt"),other=nonnegative(data,"other_parent_liabilities"),parentInterest=positive(data,"parent_interest_expense"),stake=rows.reduce((s,r)=>s+r.attributable_equity_value,0),gav=stake+parentCash;if(gav<=0)throw new RangeError("gross asset value must be positive");
const nav=gav-parentDebt-other,attributableDebt=rows.reduce((s,r)=>s+r.attributable_debt,0),enterprise=stake+attributableDebt+parentCash,leverage=enterprise>0?(parentDebt+attributableDebt)/enterprise:1,parentCoverage=rows.reduce((s,r)=>s+r.attributable_dividends,0)/parentInterest,shares=stake>0?rows.map(r=>r.attributable_equity_value/stake):[1],concentration=shares.reduce((s,v)=>s+v*v,0),freshness=stake>0?rows.filter(r=>!r.stale).reduce((s,r)=>s+r.attributable_equity_value,0)/stake:0,listed=stake>0?rows.filter(r=>r.listed).reduce((s,r)=>s+r.attributable_equity_value,0)/stake:0,navRatio=nav/gav;
const components={nav_buffer:higher(navRatio,.2,.8),lookthrough_leverage:lower(leverage,.2,.65),parent_coverage:higher(parentCoverage,1,4),diversification:lower(concentration,.25,.7),freshness:higher(freshness,.6,1),listed_coverage:higher(listed,.3,1)},score=weightedScore(components,weights),marketCap=data.parent_market_cap===undefined?null:nonnegative(data,"parent_market_cap"),discount=marketCap===null||nav<=0?null:1-marketCap/nav;
return {state:nav<=0?"nonpositive-nav-review":scoreState(score),method:"holding-company-lookthrough-score-v1",holding_ledger:rows,gross_asset_value:gav,net_asset_value:nav,attributable_subsidiary_debt:attributableDebt,lookthrough_leverage:leverage,parent_interest_coverage:parentCoverage,concentration_hhi:concentration,fresh_value_coverage:freshness,listed_value_coverage:listed,discount_to_nav:discount,component_scores:components,weights,look_through_score:score,coverage_ratio:1,reason:"attributable-stakes-with-parent-bridge"};
}
const sigmoid=(value:number):number=>value>=0?1/(1+Math.exp(-value)):Math.exp(value)/(1+Math.exp(value));
const projectSimplex=(values:number[]):number[]=>{const ordered=[...values].sort((a,b)=>b-a);let cumulative=0,rho=0;ordered.forEach((value,index)=>{cumulative+=value;if(value-(cumulative-1)/(index+1)>0)rho=index+1;});const theta=(ordered.slice(0,rho).reduce((a,b)=>a+b,0)-1)/rho,projected=values.map(v=>Math.max(v-theta,0)),total=projected.reduce((a,b)=>a+b,0);return projected.map(v=>v/total);};
const brier=(rows:number[][],labels:number[],weights:number[],intercept:number,slope:number):number=>rows.reduce((sum,row,index)=>{const score=row.reduce((s,v,j)=>s+weights[j]*v,0)/100,p=sigmoid(intercept+slope*(score-.5));return sum+(p-labels[index])**2;},0)/rows.length;
function calibrateWeights(data:RecordValue):RecordValue{
requireFramework(data,"sector-weight-calibration-teaching-v1");
const names=data.component_names,rowsRaw=data.feature_rows,labelsRaw=data.labels,datesRaw=data.observation_dates;
if(!Array.isArray(names)||names.length<2||new Set(names).size!==names.length||!names.every((n:any)=>typeof n==="string"&&n))throw new RangeError("component_names must be unique nonempty strings");
if(!Array.isArray(rowsRaw)||rowsRaw.length<12)throw new RangeError("feature_rows must contain at least 12 observations");if(!Array.isArray(labelsRaw)||labelsRaw.length!==rowsRaw.length)throw new RangeError("labels must match feature_rows");if(!Array.isArray(datesRaw)||datesRaw.length!==rowsRaw.length)throw new RangeError("observation_dates must match feature_rows");
const rows=rowsRaw.map((row:any)=>{if(!Array.isArray(row)||row.length!==names.length)throw new RangeError("each feature row must match component_names");const values=row.map((v:any)=>numberValue({v},"v"));if(values.some((v:number)=>v<0||v>100))throw new RangeError("feature scores must be within [0, 100]");return values;});
const labels=labelsRaw.map((v:any)=>{if(v!==0&&v!==1)throw new RangeError("labels must be binary 0/1 integers");return v;});const dates=datesRaw.map((v:any)=>dateValue(v,"observation_dates"));if(dates.some((v:Date,i:number)=>i<dates.length-1&&v.getTime()>=dates[i+1].getTime()))throw new RangeError("observation_dates must be strictly increasing");
const split=Math.trunc(numberValue(data,"train_end_index"));if(split<8||split>rows.length-4)throw new RangeError("train_end_index must leave at least 8 training and 4 validation rows");const baseMap=data.base_weights;if(!baseMap||typeof baseMap!=="object"||Array.isArray(baseMap)||Object.keys(baseMap).sort().join("|")!==[...names].sort().join("|"))throw new RangeError("base_weights must match component_names");const base=names.map((n:string)=>nonnegative(baseMap,n));if(Math.abs(base.reduce((a:number,b:number)=>a+b,0)-1)>1e-9)throw new RangeError("base_weights must sum to 1");
const learningRate=positive(data,"learning_rate"),ridge=nonnegative(data,"ridge_penalty"),slope=positive(data,"logit_slope"),iterations=Math.trunc(positive(data,"iterations"));if(iterations>5000)throw new RangeError("iterations must not exceed 5000");let weights=[...base],intercept=0;const trainRows=rows.slice(0,split),validationRows=rows.slice(split),trainLabels=labels.slice(0,split),validationLabels=labels.slice(split);
for(let iteration=0;iteration<iterations;iteration++){const probabilities=trainRows.map((row:number[])=>sigmoid(intercept+slope*(row.reduce((s:number,v:number,j:number)=>s+weights[j]*v,0)/100-.5))),residuals=probabilities.map((p:number,i:number)=>p-trainLabels[i]),gradIntercept=residuals.reduce((a:number,b:number)=>a+b,0)/residuals.length,gradWeights=names.map((_:string,column:number)=>residuals.reduce((sum:number,residual:number,i:number)=>sum+residual*slope*trainRows[i][column]/100,0)/trainRows.length+ridge*(weights[column]-base[column]));intercept-=learningRate*gradIntercept;weights=projectSimplex(weights.map((v:number,i:number)=>v-learningRate*gradWeights[i]));}
const baseTrain=brier(trainRows,trainLabels,base,0,slope),baseValidation=brier(validationRows,validationLabels,base,0,slope),candidateTrain=brier(trainRows,trainLabels,weights,intercept,slope),candidateValidation=brier(validationRows,validationLabels,weights,intercept,slope),improved=candidateValidation<=baseValidation,selected=improved?weights:base,selectedIntercept=improved?intercept:0,selectedValidation=improved?candidateValidation:baseValidation;
return {state:improved?"calibrated-improved":"retain-base-weights",method:"nonnegative-simplex-logloss-v1",component_names:names,base_weights:Object.fromEntries(names.map((n:string,i:number)=>[n,base[i]])),candidate_weights:Object.fromEntries(names.map((n:string,i:number)=>[n,weights[i]])),selected_weights:Object.fromEntries(names.map((n:string,i:number)=>[n,selected[i]])),candidate_intercept:intercept,selected_intercept:selectedIntercept,base_train_brier:baseTrain,base_validation_brier:baseValidation,candidate_train_brier:candidateTrain,candidate_validation_brier:candidateValidation,selected_validation_brier:selectedValidation,weight_shift_l1:weights.reduce((s:number,v:number,i:number)=>s+Math.abs(v-base[i]),0),train_rows:trainRows.length,validation_rows:validationRows.length,coverage_ratio:1,reason:"temporal-holdout-governs-selection"};
}
const ROUTES:Record<string,[string,string,string[]]>={bank:["D18-F10-A01","basel-iii-teaching-v1",["cet1_ratio","leverage_ratio","lcr","nsfr","npl_ratio","provision_coverage_ratio","net_interest_margin","cost_income_ratio"]],insurance:["D18-F10-A02","solvency-ii-nonlife-teaching-v1",["scr_coverage_ratio","mcr_coverage_ratio","combined_ratio","adverse_reserve_development_ratio","tier1_own_funds_share","investment_concentration_ratio","return_on_equity"]],reit:["D18-F10-A03","nareit-equity-reit-teaching-v1",["nareit_ffo","recurring_capex","common_dividends","net_debt","ebitda_re","interest_expense","occupancy_ratio","same_store_noi_growth"]],utility:["D18-F10-A04","ferc-regulated-electric-teaching-v1",["allowed_roe","earned_roe","funds_from_operations","total_debt","debt_to_capital","ebit","interest_expense","capital_expenditure"]],"early-stage":["D18-F10-A05","early-stage-liquidity-teaching-v1",["unrestricted_cash","liquid_investments","monthly_net_cash_flows","near_term_obligations"]],cyclical:["D18-F10-A06","cyclical-midcycle-teaching-v1",["realized_price_history","unit_cost_history","volume_history","free_cash_flow_history","net_debt"]],"holding-company":["D18-F10-A07","holding-company-lookthrough-teaching-v1",["holdings","parent_cash","parent_debt","parent_interest_expense"]]};
function coverageDecision(data:RecordValue):RecordValue{
requireFramework(data,"coverage-router-teaching-v1");const sector=textValue(data,"sector"),candidate=textValue(data,"candidate_framework"),asOf=dateValue(data.as_of,"as_of"),minimum=numberValue(data,"minimum_coverage"),maxAge=Math.trunc(positive(data,"max_age_days"));if(!(minimum>0&&minimum<=1))throw new RangeError("minimum_coverage must be in (0, 1]");if(!ROUTES[sector])return{state:"abstain",method:"sector-coverage-router-v1",selected_model:null,coverage_ratio:0,available_fields:[],missing_fields:[],stale_fields:[],future_fields:[],reasons:["unsupported-sector"],reason:"unsupported-sector"};
const [model,expected,required]=ROUTES[sector];if(candidate!==expected)return{state:"abstain",method:"sector-coverage-router-v1",selected_model:null,coverage_ratio:0,available_fields:[],missing_fields:[...required],stale_fields:[],future_fields:[],reasons:["framework-mismatch"],reason:"framework-mismatch"};const facts=data.facts;if(!Array.isArray(facts))throw new TypeError("facts must be an array");const ledger:Record<string,any>={};for(const raw of facts){if(!raw||typeof raw!=="object"||Array.isArray(raw))throw new TypeError("each fact must be an object");const name=textValue(raw,"name");if(ledger[name])throw new RangeError("fact names must be unique");if(typeof raw.value_present!=="boolean")throw new TypeError("value_present must be boolean");ledger[name]=raw;}
const available:string[]=[],missing:string[]=[],stale:string[]=[],future:string[]=[];for(const name of required){const fact=ledger[name];if(!fact||!fact.value_present){missing.push(name);continue;}const knowledge=dateValue(fact.knowledge_date,`${name}.knowledge_date`),periodEnd=dateValue(fact.period_end,`${name}.period_end`);if(knowledge.getTime()>asOf.getTime())future.push(name);else if((asOf.getTime()-periodEnd.getTime())/86400000>maxAge)stale.push(name);else available.push(name);}const coverage=available.length/required.length,reasons:string[]=[];if(future.length)reasons.push("future-evidence");if(stale.length)reasons.push("stale-evidence");if(missing.length)reasons.push("missing-required-fields");let state:string,selected:string|null;if(future.length){state="abstain";selected=null;}else if(coverage===1){state="supported";selected=model;}else if(coverage>=minimum){state="partial-review";selected=model;}else{state="abstain";selected=null;reasons.push("coverage-below-minimum");}if(!reasons.length)reasons.push("complete-current-coverage");return{state,method:"sector-coverage-router-v1",selected_model:selected,coverage_ratio:coverage,available_fields:available,missing_fields:missing,stale_fields:stale,future_fields:future,required_field_count:required.length,reasons,reason:reasons[0]};
}
export function calculate(topicId:string,data:RecordValue):RecordValue{
if(!data||typeof data!=="object"||Array.isArray(data))throw new TypeError("input must be an object");
const functions:Record<string,(value:RecordValue)=>RecordValue>={"D18-F10-A01":bankScore,"D18-F10-A02":insuranceScore,"D18-F10-A03":reitScore,"D18-F10-A04":utilityScore,"D18-F10-A05":earlyStageScore,"D18-F10-A06":cyclicalScore,"D18-F10-A07":holdingCompanyScore,"D18-F10-A08":calibrateWeights,"D18-F10-A09":coverageDecision};
if(!functions[topicId])throw new RangeError(`unsupported topic ID: ${topicId}`);return functions[topicId](data);
}
The embedded lab now expands to its full document height, keeping the article as the only scroll surface.