Psychological Round-Number Level Generation

Generate an explicit, currency-aware round-number grid instead of guessing visually salient prices.

The decision this tutorial makes visible

For multi-asset scanners and UI builders, a level is psychologically round only relative to a declared quotation unit and tick table—not because its decimal representation looks simple.

The precise question is: Which tick-aligned round-number candidates exist inside a declared range and how are major, half, and minor multiples classified?

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

Roundness depends on quotation scale. The algorithm exposes the chosen unit before it labels any candidate as psychologically salient.

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

A caller-configured base unit, finite bounds, tick-aligned levels, and deterministic salience classes.

Variant	Definition	Best use	Main limitation
Canonical repository convention	A caller-configured base unit, finite bounds, tick-aligned levels, and deterministic salience classes.	Reproducible teaching and reference implementation	Requires calibration before empirical use
Platform-specific implementation	Vendor-selected defaults, data resolution, and ties	Parity with one named platform	Not portable without a parity specification
Discretionary chart annotation	Human-selected levels and context	Exploratory review	Not reproducible without a written rubric

What is sourced, selected, synthetic, and derived

Role	Material claim	Evidence	Boundary
Primary empirical research	Reports clustering of requested execution rates at round numbers in the studied FX order data and connects those clusters with support/resistance practice.	S1 exact source record	It does not validate a universal grid, every asset class, future reactions, or this package's salience weights.
Primary computational technical-analysis research	Shows why subjective chart concepts require explicit computational definitions and separates pattern recognition from statistical evaluation.	S2 exact source record	It does not define this family's zone algorithms or establish current out-of-sample economic value.
Implementation choice	A caller-configured base unit, finite bounds, tick-aligned levels, and deterministic salience classes.	Frozen definition contract, formula, fixtures, and parity tests	This is the package convention, not a universal definition.
Synthetic teaching input	Every displayed price, trade, profile, touch, bar, zone, and instrument snapshot is repository-authored.	datasets/canonical-input.json and scenario-results.json	No value is presented as an observed security or provider record.
Author-derived calculation	The canonical fixture produces all configured grid levels plus the nearest deterministically tie-broken candidate.	Formula, expected output, examples, and cross-language parity	Calculation correctness does not establish predictive or economic value.

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

Plain text

L_n = n u; class(n) = major if n mod 10=0, half if n mod 5=0, otherwise minor

Symbol	Meaning	Unit	Policy
u	configured base unit	price	tick aligned
n	integer grid multiple	count	covers bounds
L_n	round-number level	price	n times u
d_n	distance to current price	price/bps	absolute

Prices and tolerances share one currency, adjustment basis, and tick table.
the base unit must itself be an integer number of ticks.
Published values use full-precision calculation and explicit display rounding; no hidden epsilon changes a decision.
Ties are broken deterministically and preserved in the audit output.

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

Validate current price, ordered bounds, tick size, and base unit
Convert bounds and base unit to integer ticks
Enumerate in-range multiples of the base unit
Classify each multiple and calculate price/bps distance
Choose distance, then salience, then lower-price deterministically

Production-minded operational checklist

Store currency, quote convention, tick-table version, base unit, and bounds with the generated level set.
Partition by instrument, venue/session, currency, interval, and adjustment basis.
Persist code version, source records, inputs, output diagnostics, and tie decisions.
Evaluate empirical association separately with costs, leakage controls, and out-of-sample data.

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, closest_level, is all configured grid levels plus the nearest deterministically tie-broken candidate. The complete input and output are in datasets/canonical-input.json and datasets/expected-output.json.

The labeled synthetic canonical fixture applies L_n = n u; class(n) = major if n mod 10=0, half if n mod 5=0, otherwise minor and returns all configured grid levels plus the nearest deterministically tie-broken candidate. The expected JSON is generated once from the frozen contract and independently checked in both language implementations.

Counterfactual checkpoint

Psychological Round-Number Level Generation boundary case. A different quote scale or base unit produces a different set and class hierarchy. The output changes because Reproducibility requires counterfactual behavior at the boundary.

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 current-price sweep	Step 30 · canonical fixture	Move current price around the exact canonical fixture on the one-unit grid.	calculated	closest 103.00	State calculated; closest 103.00.	1
Equal-distance lower-price tie	Step 30 · comparison focus	Cross the midpoint between two equally salient minor levels.	calculated	closest 103.00	State calculated; closest 103.00.	1
Narrow bounded grid	Step 30 · comparison focus	Restrict generation to a valid narrow range around the current price.	calculated	closest 103.00	State calculated; closest 103.00.	1
Half-unit quote grid	Step 30 · comparison focus	Change the configured base unit from 1.00 to 0.50.	calculated	closest 103.00	State calculated; closest 103.00.	1
Major-versus-minor salience tie	Step 30 · comparison focus	Cross the equal-distance midpoint between 99 minor and 100 major.	calculated	closest 100.00	State calculated; closest 100.00.	1
Bounds exclude outer levels	Step 30 · comparison focus	Use non-round bounds so only fully in-range grid multiples are emitted.	calculated	closest 103.00	State calculated; closest 103.00.	1
Wide five-unit scale	Step 30 · comparison focus	Generate a broad valid grid with a five-unit base scale.	calculated	closest 100.00	State calculated; closest 100.00.	1

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

Psychological Round-Number Level Generation annotated teaching map

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:

Input or clock contract fails — Reject, because A precise output would be misleading.
the base unit must itself be an integer number of ticks — Apply the declared equality/tie policy, because Boundary behavior must be reproducible.
Valid evidence does not satisfy the algorithm — Return a valid rejection, empty set, or nonconfirmed state, because Absence is different from invalid data.
All required conditions pass — Return the structured result and diagnostics, because The frozen contract is satisfied.

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:

Return a named state rather than a bare scalar when decisions are sequential.
Preserve source IDs, members, expansion order, component scores, or state transitions where applicable.
Keep point-in-time cutoffs and selected parameters beside the output.
Separate invalid input from a valid nonmatch, rejection, or empty eligible result.

Passing definition and parity checks proves that the implementation matches the selected contract. It does not prove production performance, universal applicability, or a later market outcome.

Failure modes and misuse

Empirical clustering documented in one FX dataset does not establish the same unit, class weights, or reactions for every instrument.
Platform and analyst conventions can produce different results from the same chart.
A recognized level interaction is not evidence of future association or economic value.
The output is educational analytics, not investment advice or an order instruction.

Debugging order

When a result looks surprising, inspect the state in this order:

Confirm identifiers, scope, side, and decision clock.
Confirm units, ordering, and point-in-time inputs.
Confirm equality, rounding, null, and reset policies.
Recalculate the invariant and declared scenario focus before changing code.

Evidence and historical boundary

Historical decision: not useful. A named chart occurrence would add narrative appeal without improving reproducibility. Classification changes with provider, session, adjustment basis, tick table, anchors, thresholds, and the point-in-time record available to the detector.

The primary sources are New York Fed round-number evidence, Lo–Mamaysky–Wang. 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 implement, inspect, and validate Psychological Round-Number Level Generation with its full topic-specific audit evidence. The learning flow is: Fibonacci Retracement and Extension Projection → Psychological Round-Number Level Generation → Multi-Source Support/Resistance Zone Fusion. Carry the result forward only with its scope, clock, state, and evidence label.

Workflows

Rendered from the canonical Mermaid sources linked by this article.

Psychological Round-Number Level Generation calculation flow

This flow identifies the selected calculation stages and the structured output.

Rendering system map…

Takeaway: Roundness is a configured property of the quote grid; distance and salience are separate, auditable ranking terms.

ReferencesPrimary sources and evidence notes

Expand the source trail, evidence role, and limitations behind the engineering choices.

S1 — Currency Orders and Exchange-Rate Dynamics: Explaining the Success of Technical Analysis

Organization or authors: Carol L. Osler
Source type: Federal Reserve Bank of New York Staff Report 125
Publication or effective date: Published April 2001; accessed 2026-08-03
Version: Staff Report 125
URL or DOI: https://www.newyorkfed.org/medialibrary/media/research/staff_reports/sr125.html
Accessed: 2026-08-03
Jurisdiction: Foreign-exchange dealer order data studied in the paper
Supports: Reports clustering of requested execution rates at round numbers in the studied FX order data and connects those clusters with support/resistance practice.
Limitations: It does not validate a universal grid, every asset class, future reactions, or this package's salience weights.

S2 — Foundations of Technical Analysis: Computational Algorithms, Statistical Inference, and Empirical Implementation

Organization or authors: Andrew W. Lo, Harry Mamaysky, and Jiang Wang
Source type: Original NBER working paper and Journal of Finance study
Publication or effective date: Working Paper 7613, March 2000; accessed 2026-08-03
Version: NBER Working Paper 7613
URL or DOI: https://www.nber.org/papers/w7613
Accessed: 2026-08-03
Jurisdiction: U.S. equity sample described by the paper
Supports: Shows why subjective chart concepts require explicit computational definitions and separates pattern recognition from statistical evaluation.
Limitations: It does not define this family's zone algorithms or establish current out-of-sample economic value.

Evidence boundary

The sources establish the exact rule, interface, protocol, or research context named above. They do not verify the repository-authored synthetic fixture, thresholds, empirical usefulness, execution probability, or profitability. Package-selected choices remain labeled as implementation choices wherever they are used.

Implementation

Full dependency-light reference implementations in both supported languages.

level-confluence.ts

/** Reference algorithms for D08-F06. Repository teaching conventions only. */

type Row = Record<string, any>;

function numberValue(value: unknown, name: string, minimum?: number): number {
  if (typeof value !== "number" || !Number.isFinite(value)) throw new TypeError(`${name} must be a finite number`);
  if (minimum !== undefined && value < minimum) throw new RangeError(`${name} must be >= ${minimum}`);
  return value;
}

function integerValue(value: unknown, name: string, minimum = 0): number {
  const result = numberValue(value, name);
  if (!Number.isInteger(result) || result < minimum) throw new RangeError(`${name} must be an integer >= ${minimum}`);
  return result;
}

function timeValue(value: unknown, name: string): number {
  if (typeof value !== "string" || !/(Z|[+-]\d\d:\d\d)$/.test(value)) throw new TypeError(`${name} must be a zoned ISO-8601 string`);
  const result = Date.parse(value);
  if (!Number.isFinite(result)) throw new RangeError(`${name} must be a zoned ISO-8601 string`);
  return result;
}

function rounded(value: number): number { return Number(value.toFixed(12)); }

function alignedTicks(price: unknown, tick: number, name: string): number {
  const value = numberValue(price, name);
  const ticks = Math.round(value / tick);
  if (Math.abs(value - ticks * tick) > tick * 1e-8) throw new RangeError(`${name} must align to tick_size`);
  return ticks;
}

function median(values: number[]): number {
  const ordered = [...values].sort((a, b) => a - b);
  const middle = Math.floor(ordered.length / 2);
  return ordered.length % 2 ? ordered[middle] : (ordered[middle - 1] + ordered[middle]) / 2;
}

function profile(input: Row): Row {
  const tick = numberValue(input.tick_size, "tick_size", 1e-12);
  const widthTicks = integerValue(input.bin_size_ticks, "bin_size_ticks", 1);
  const windowEnd = timeValue(input.window_end, "window_end");
  if (!Array.isArray(input.trades) || input.trades.length === 0) throw new RangeError("trades must be non-empty");
  const seen = new Set<string>();
  const volumes = new Map<number, number>();
  let previous: number | null = null, total = 0, eligible = 0;
  input.trades.forEach((trade: Row, index: number) => {
    if (!trade || typeof trade !== "object") throw new TypeError("each trade must be an object");
    if (typeof trade.trade_id !== "string" || !trade.trade_id || seen.has(trade.trade_id)) throw new RangeError("trade_id must be unique");
    seen.add(trade.trade_id);
    if (trade.final !== true) throw new RangeError("all trades must be final");
    const timestamp = timeValue(trade.timestamp, `trades[${index}].timestamp`);
    if (timestamp > windowEnd || (previous !== null && timestamp < previous)) throw new RangeError("trades must be ordered and available");
    previous = timestamp;
    const priceTicks = alignedTicks(trade.price, tick, `trades[${index}].price`);
    const volume = numberValue(trade.volume, `trades[${index}].volume`, 0);
    if (volume === 0) return;
    eligible += 1; total += volume;
    const binIndex = Math.floor(priceTicks / widthTicks);
    volumes.set(binIndex, (volumes.get(binIndex) ?? 0) + volume);
  });
  if (total <= 0) throw new RangeError("eligible volume must be positive");
  const rows = [...volumes.keys()].sort((a, b) => a - b).map(binIndex => {
    const lowerTicks = binIndex * widthTicks, lower = lowerTicks * tick, upper = (lowerTicks + widthTicks) * tick;
    const volume = volumes.get(binIndex)!;
    return { bin_index: binIndex, lower: rounded(lower), upper: rounded(upper), midpoint: rounded((lower + upper) / 2), volume: rounded(volume), share: rounded(volume / total) };
  });
  return { state: "calculated", tick_size: tick, bin_size_ticks: widthTicks, bin_width: rounded(widthTicks * tick), total_volume: rounded(total), trade_count: input.trades.length, eligible_trade_count: eligible, rows };
}

function profileFeatures(input: Row): Row {
  if (!Array.isArray(input.profile_rows) || input.profile_rows.length < 3) throw new RangeError("profile_rows must contain at least three rows");
  const fraction = numberValue(input.value_area_fraction, "value_area_fraction");
  const hvnRatio = numberValue(input.hvn_median_ratio, "hvn_median_ratio", 1);
  const lvnRatio = numberValue(input.lvn_median_ratio, "lvn_median_ratio");
  if (!(fraction > 0 && fraction <= 1) || lvnRatio < 0 || lvnRatio > 1) throw new RangeError("fractions outside canonical range");
  let previousUpper: number | null = null;
  const rows = input.profile_rows.map((row: Row, index: number) => {
    const lower = numberValue(row.lower, `profile_rows[${index}].lower`), upper = numberValue(row.upper, `profile_rows[${index}].upper`), volume = numberValue(row.volume, `profile_rows[${index}].volume`, 0);
    if (upper <= lower || (previousUpper !== null && Math.abs(lower - previousUpper) > 1e-9)) throw new RangeError("profile rows must be ordered and contiguous");
    previousUpper = upper; return { lower, upper, midpoint: (lower + upper) / 2, volume };
  });
  const total = rows.reduce((sum: number, row: Row) => sum + row.volume, 0);
  if (total <= 0) throw new RangeError("profile volume must be positive");
  const profileMidpoint = (rows[0].lower + rows[rows.length - 1].upper) / 2;
  const maximum = Math.max(...rows.map((row: Row) => row.volume));
  const candidates = rows.map((row: Row, i: number) => row.volume === maximum ? i : -1).filter((i: number) => i >= 0);
  candidates.sort((a: number, b: number) => Math.abs(rows[a].midpoint - profileMidpoint) - Math.abs(rows[b].midpoint - profileMidpoint) || rows[a].midpoint - rows[b].midpoint);
  const pocIndex = candidates[0], included = new Set<number>([pocIndex]), trace = [pocIndex];
  let cumulative = rows[pocIndex].volume, low = pocIndex, high = pocIndex;
  const target = total * fraction;
  while (cumulative < target && (low > 0 || high < rows.length - 1)) {
    const below = low > 0 ? low - 1 : null, above = high < rows.length - 1 ? high + 1 : null;
    let chosen: number;
    if (below === null) chosen = above!; else if (above === null) chosen = below; else chosen = rows[above].volume >= rows[below].volume ? above : below;
    included.add(chosen); cumulative += rows[chosen].volume; low = Math.min(low, chosen); high = Math.max(high, chosen); trace.push(chosen);
  }
  const positiveMedian = median(rows.filter((row: Row) => row.volume > 0).map((row: Row) => row.volume));
  const hvn: Row[] = [], lvn: Row[] = [];
  for (let i = 1; i < rows.length - 1; i += 1) {
    const current = rows[i].volume, item = { price: rounded(rows[i].midpoint), volume: rounded(current), median_ratio: rounded(current / positiveMedian) };
    if (current > rows[i - 1].volume && current >= rows[i + 1].volume && current >= positiveMedian * hvnRatio) hvn.push(item);
    if (current < rows[i - 1].volume && current <= rows[i + 1].volume && current <= positiveMedian * lvnRatio) lvn.push(item);
  }
  return { state: "calculated", poc_index: pocIndex, poc_price: rounded(rows[pocIndex].midpoint), poc_volume: rounded(maximum), value_area_low: rounded(rows[low].lower), value_area_high: rounded(rows[high].upper), value_area_volume: rounded(cumulative), value_area_share: rounded(cumulative / total), target_share: fraction, included_indices: [...included].sort((a, b) => a - b), expansion_trace: trace, hvn, lvn };
}

function fibonacci(input: Row): Row {
  const start = numberValue(input.start_price, "start_price"), end = numberValue(input.end_price, "end_price"), correction = numberValue(input.retracement_end_price, "retracement_end_price"), tick = numberValue(input.tick_size, "tick_size", 1e-12);
  if (start === end || !Array.isArray(input.retracement_ratios) || !input.retracement_ratios.length || !Array.isArray(input.extension_ratios) || !input.extension_ratios.length) throw new RangeError("invalid anchors or ratios");
  const rr = input.retracement_ratios.map((v: unknown) => numberValue(v, "retracement ratio")), er = input.extension_ratios.map((v: unknown) => numberValue(v, "extension ratio"));
  if (rr.some((v: number) => v < 0 || v > 1) || er.some((v: number) => v < 0)) throw new RangeError("ratios outside canonical ranges");
  const direction = end > start ? 1 : -1, magnitude = Math.abs(end - start), snap = (value: number) => {
    const tickUnits = value / tick, roundedUnits = Math.sign(tickUnits) * Math.floor(Math.abs(tickUnits) + 0.5);
    return rounded(roundedUnits * tick);
  };
  return { state: "calculated", direction: direction > 0 ? "up" : "down", leg_size: rounded(magnitude), retracement_levels: rr.map((ratio: number) => ({ ratio, raw_price: rounded(end - direction * ratio * magnitude), price: snap(end - direction * ratio * magnitude) })), extension_levels: er.map((ratio: number) => ({ ratio, raw_price: rounded(correction + direction * ratio * magnitude), price: snap(correction + direction * ratio * magnitude) })), rounding: "nearest tick, half away from zero" };
}

function roundNumbers(input: Row): Row {
  const current = numberValue(input.current_price, "current_price"), lower = numberValue(input.lower_bound, "lower_bound"), upper = numberValue(input.upper_bound, "upper_bound"), tick = numberValue(input.tick_size, "tick_size", 1e-12), unit = numberValue(input.base_unit, "base_unit", tick);
  if (lower > current || current > upper || lower >= upper) throw new RangeError("invalid bounds");
  const unitTicks = alignedTicks(unit, tick, "base_unit"), lowerTicks = Math.ceil(lower / tick - 1e-9), upperTicks = Math.floor(upper / tick + 1e-9), first = Math.ceil(lowerTicks / unitTicks) * unitTicks;
  const levels: Row[] = [];
  for (let priceTicks = first; priceTicks <= upperTicks; priceTicks += unitTicks) {
    const multiple = Math.round(priceTicks / unitTicks), major = multiple % 10 === 0, half = multiple % 5 === 0, price = priceTicks * tick, weight = major ? 1 : half ? 0.75 : 0.5;
    levels.push({ price: rounded(price), class: major ? "major" : half ? "half" : "minor", salience_weight: weight, distance: rounded(Math.abs(price - current)), distance_bps: current === 0 ? null : rounded(Math.abs(price - current) / Math.abs(current) * 10000) });
  }
  if (!levels.length) throw new RangeError("bounds contain no levels");
  const closest = [...levels].sort((a, b) => a.distance - b.distance || b.salience_weight - a.salience_weight || a.price - b.price)[0];
  return { state: "calculated", base_unit: unit, level_count: levels.length, closest_level: closest, levels };
}

function fusion(input: Row): Row {
  if (!Array.isArray(input.levels) || !input.levels.length) throw new RangeError("levels must be non-empty");
  const tolerance = numberValue(input.fusion_tolerance, "fusion_tolerance", 0), minimumSources = integerValue(input.minimum_sources, "minimum_sources", 1), seen = new Set<string>();
  const parsed = input.levels.map((level: Row, index: number) => {
    if (typeof level.level_id !== "string" || !level.level_id || seen.has(level.level_id) || typeof level.source !== "string" || !level.source) throw new RangeError("level identity/source invalid");
    seen.add(level.level_id); return { level_id: level.level_id, source: level.source, price: numberValue(level.price, `levels[${index}].price`), weight: numberValue(level.weight, `levels[${index}].weight`, 0) };
  }).sort((a: Row, b: Row) => a.price - b.price || a.source.localeCompare(b.source) || a.level_id.localeCompare(b.level_id));
  const clusters: Row[][] = [];
  parsed.forEach((level: Row) => { if (!clusters.length || level.price - clusters[clusters.length - 1][0].price > 2 * tolerance) clusters.push([level]); else clusters[clusters.length - 1].push(level); });
  const zones: Row[] = [], rejected_clusters: Row[] = [];
  clusters.forEach((cluster, index) => {
    const sources = [...new Set(cluster.map(row => row.source))].sort(), weightSum = cluster.reduce((sum, row) => sum + row.weight, 0), center = weightSum > 0 ? cluster.reduce((sum, row) => sum + row.price * row.weight, 0) / weightSum : cluster.reduce((sum, row) => sum + row.price, 0) / cluster.length;
    const item = { zone_id: `Z${String(index + 1).padStart(2, "0")}`, lower: rounded(Math.min(...cluster.map(row => row.price)) - tolerance), upper: rounded(Math.max(...cluster.map(row => row.price)) + tolerance), center: rounded(center), source_count: sources.length, sources, weight_sum: rounded(weightSum), member_ids: cluster.map(row => row.level_id) };
    if (sources.length >= minimumSources) zones.push(item); else rejected_clusters.push({ ...item, reason: "insufficient-distinct-sources" });
  });
  zones.sort((a, b) => b.source_count - a.source_count || b.weight_sum - a.weight_sum || a.center - b.center);
  return { state: "calculated", zones, rejected_clusters, fusion_tolerance: tolerance, minimum_sources: minimumSources };
}

function strength(input: Row): Row {
  const source = numberValue(input.source_confluence, "source_confluence"), age = integerValue(input.zone_age_bars, "zone_age_bars"), halfLife = numberValue(input.half_life_bars, "half_life_bars", 1e-12), breakCount = integerValue(input.break_count, "break_count"), rejectionTarget = numberValue(input.rejection_target_atr, "rejection_target_atr", 1e-12);
  if (source < 0 || source > 1 || !Array.isArray(input.touches)) throw new RangeError("invalid source or touches");
  const decayed = input.touches.map((touch: Row, index: number) => { const touchAge = integerValue(touch.age_bars, `touches[${index}].age_bars`), rejection = numberValue(touch.rejection_atr, `touches[${index}].rejection_atr`, 0); return [0.5 ** (touchAge / halfLife), Math.min(rejection / rejectionTarget, 1)]; });
  const evidence = decayed.reduce((sum: number, value: number[]) => sum + value[0], 0), sourceComponent = 30 * source, touchComponent = 35 * (1 - Math.exp(-evidence)), rejectionComponent = evidence === 0 ? 0 : 25 * decayed.reduce((sum: number, value: number[]) => sum + value[0] * value[1], 0) / evidence, durabilityComponent = 10 * (0.5 ** (age / halfLife)), penalty = Math.min(30, 15 * breakCount), score = Math.max(0, Math.min(100, sourceComponent + touchComponent + rejectionComponent + durabilityComponent - penalty));
  return { state: "calculated", score: rounded(score), grade: score >= 75 ? "strong" : score >= 50 ? "moderate" : score >= 25 ? "weak" : "depleted", components: { source: rounded(sourceComponent), touch: rounded(touchComponent), rejection: rounded(rejectionComponent), durability: rounded(durabilityComponent), break_penalty: rounded(penalty) }, decayed_touch_evidence: rounded(evidence), touch_count: input.touches.length };
}

function roleReversal(input: Row): Row {
  const lower = numberValue(input.zone_lower, "zone_lower"), upper = numberValue(input.zone_upper, "zone_upper"), buffer = numberValue(input.break_buffer, "break_buffer", 0), confirmations = integerValue(input.confirmation_closes, "confirmation_closes", 1);
  if (lower >= upper || !["support", "resistance"].includes(input.initial_role) || !Array.isArray(input.closes) || !input.closes.length) throw new RangeError("invalid role-reversal input");
  const values = input.closes.map((value: unknown) => numberValue(value, "close")); let role = input.initial_role, state = `active-${role}`, outsideCount = 0, retestSeen = false; const transitions: Row[] = [];
  values.forEach((close: number, index: number) => {
    const side = close > upper + buffer ? "above" : close < lower - buffer ? "below" : "zone", previous = state;
    if (state === "active-support") { outsideCount = side === "below" ? outsideCount + 1 : 0; if (outsideCount >= confirmations) { state = "awaiting-resistance-retest"; outsideCount = 0; } }
    else if (state === "active-resistance") { outsideCount = side === "above" ? outsideCount + 1 : 0; if (outsideCount >= confirmations) { state = "awaiting-support-retest"; outsideCount = 0; } }
    else if (state === "awaiting-resistance-retest") { if (side === "zone") retestSeen = true; else if (retestSeen && side === "below") { state = "confirmed-resistance"; role = "resistance"; } else if (side === "above") state = "invalidated"; }
    else if (state === "awaiting-support-retest") { if (side === "zone") retestSeen = true; else if (retestSeen && side === "above") { state = "confirmed-support"; role = "support"; } else if (side === "below") state = "invalidated"; }
    if (state !== previous) transitions.push({ index, close, from: previous, to: state, side });
  });
  return { state, final_role: state === "invalidated" ? "none" : role, confirmed: state.startsWith("confirmed-"), retest_seen: retestSeen, transitions, observations: values.length };
}

function breakoutRetest(input: Row): Row {
  const lower = numberValue(input.zone_lower, "zone_lower"), upper = numberValue(input.zone_upper, "zone_upper"), buffer = numberValue(input.break_buffer, "break_buffer", 0), tolerance = numberValue(input.retest_tolerance, "retest_tolerance", 0), needed = integerValue(input.breakout_closes, "breakout_closes", 1), maxBars = integerValue(input.max_retest_bars, "max_retest_bars", 1), direction = input.direction;
  if (lower >= upper || !["up", "down"].includes(direction) || !Array.isArray(input.bars) || !input.bars.length) throw new RangeError("invalid breakout input");
  let state = "searching", count = 0, breakout_index: number | null = null, retest_index: number | null = null, confirmation_index: number | null = null; const transitions: Row[] = [];
  input.bars.forEach((bar: Row, index: number) => {
    const high = numberValue(bar.high, "bar.high"), low = numberValue(bar.low, "bar.low"), close = numberValue(bar.close, "bar.close");
    if (high < Math.max(low, close) || low > Math.min(high, close)) throw new RangeError("inconsistent bar");
    const previous = state, beyond = direction === "up" ? close > upper + buffer : close < lower - buffer, failed = direction === "up" ? close < lower - buffer : close > upper + buffer, contact = low <= upper + tolerance && high >= lower - tolerance;
    if (state === "searching" || state === "breakout-pending") { count = beyond ? count + 1 : 0; state = count ? "breakout-pending" : "searching"; if (count >= needed) { breakout_index = index; state = "awaiting-retest"; } }
    else if (state === "awaiting-retest") { if (breakout_index !== null && index - breakout_index > maxBars) state = "expired"; else if (failed) state = "failed"; else if (contact) { retest_index = index; state = "retest-contact"; } }
    else if (state === "retest-contact") { if (failed) state = "failed"; else if (beyond) { confirmation_index = index; state = "confirmed"; } else if (breakout_index !== null && index - breakout_index > maxBars) state = "expired"; }
    if (state !== previous) transitions.push({ index, from: previous, to: state, close });
  });
  return { state, confirmed: state === "confirmed", direction, breakout_index, retest_index, confirmation_index, transitions };
}

function scanner(input: Row): Row {
  const asOf = timeValue(input.as_of, "as_of"), maxBps = numberValue(input.max_distance_bps, "max_distance_bps", 0), halfLife = numberValue(input.freshness_half_life_hours, "freshness_half_life_hours", 1e-12);
  if (!Array.isArray(input.instruments) || !input.instruments.length) throw new RangeError("instruments must be non-empty");
  const seen = new Set<string>(), ranked: Row[] = [];
  input.instruments.forEach((item: Row, index: number) => {
    if (typeof item.instrument_id !== "string" || !item.instrument_id || seen.has(item.instrument_id)) throw new RangeError("instrument_id must be unique"); seen.add(item.instrument_id);
    const price = numberValue(item.current_price, `instruments[${index}].current_price`, 1e-12), lower = numberValue(item.zone_lower, "zone_lower"), upper = numberValue(item.zone_upper, "zone_upper"), zoneStrength = numberValue(item.zone_strength, "zone_strength"), observed = timeValue(item.observed_at, "observed_at");
    if (lower >= upper || zoneStrength < 0 || zoneStrength > 100 || observed > asOf) throw new RangeError("invalid point-in-time zone record");
    const distance = price < lower ? lower - price : price > upper ? price - upper : 0, distanceBps = distance / price * 10000, ageHours = (asOf - observed) / 3600000, freshness = 0.5 ** (ageHours / halfLife), proximity = maxBps > 0 ? Math.max(0, 1 - distanceBps / maxBps) : distanceBps === 0 ? 1 : 0, score = 100 * (0.55 * proximity + 0.30 * zoneStrength / 100 + 0.15 * freshness);
    if (distanceBps <= maxBps) ranked.push({ instrument_id: item.instrument_id, current_price: price, zone_lower: lower, zone_upper: upper, inside_zone: distance === 0, distance: rounded(distance), distance_bps: rounded(distanceBps), strength: zoneStrength, freshness: rounded(freshness), rank_score: rounded(score) });
  });
  ranked.sort((a, b) => b.rank_score - a.rank_score || a.distance_bps - b.distance_bps || a.instrument_id.localeCompare(b.instrument_id)); ranked.forEach((row, index) => { row.rank = index + 1; });
  return { state: "calculated", as_of: input.as_of, eligible_count: ranked.length, ranked };
}

const calculators: Record<string, (input: Row) => Row> = {
  "D08-F06-A01": profile,
  "D08-F06-A02": profileFeatures,
  "D08-F06-A03": fibonacci,
  "D08-F06-A04": roundNumbers,
  "D08-F06-A05": fusion,
  "D08-F06-A06": strength,
  "D08-F06-A07": roleReversal,
  "D08-F06-A08": breakoutRetest,
  "D08-F06-A09": scanner,
};

export function calculate(topicId: string, input: Row): Row {
  const calculator = calculators[topicId];
  if (!calculator) throw new RangeError(`unsupported topic_id: ${topicId}`);
  if (!input || typeof input !== "object" || Array.isArray(input)) throw new TypeError("inputs must be an object");
  return calculator(input);
}

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