D12-F03-A01 / Complete engineering topic

Tick-Size Validation

A production-minded guide to Tick-Size Validation.

D12 · MATCHING ENGINES AND VENUE LO…
D12-F03-A01Canonical / Tested / Open
D12 / D12-F03

Reject off-grid prices without floating-point ambiguity and report the neighboring valid prices.

The decision this tutorial makes visible

Matching engines cannot safely rank or acknowledge a price until it conforms to the effective instrument grid.

The precise question is: Does an integer-scaled order price lie exactly on the tick grid effective for this instrument and policy date?

An operator needs a deterministic accept, reject, prevent, purge, or trigger decision with its exact reason. A builder needs the same point-in-time policy and order state to reproduce that decision in code, audit data, visuals, and the browser lab.

Intuition before notation

A tick grid is a ruler. Integer atoms make the question exact: either the price lands on a mark or it has a measurable remainder.

The result depends on instrument and venue scope, effective policy identity, session ownership, decision-time reference state, equality rules, and exact units. Changing any one of them creates a different control decision even when the output field name is unchanged.

Scope and nearby methods

The canonical validator receives an already-resolved tick size and policy ID, then applies exact integer divisibility. It does not infer a regulatory tick from price alone.

VariantDefinitionBest useMain limitation
Explicit resolved tickCaller supplies the effective tickDeterministic gateway validationDoes not resolve the tick
Regulatory tick assignmentDerive tick from rule-specific market statisticsReference-data serviceMaterially different algorithm
Venue product tableUse venue/product price bands and incrementsDerivatives and optionsNot universal

What is sourced, selected, synthetic, and derived

RoleMaterial claimEvidenceBoundary
Sourced factSEC Rule 612 governs minimum pricing increments for covered NMS-stock quotations and orders; the 2024 amended half-cent regime for certain stocks is under temporary relief until the first business day of November 2027.S1The SEC source does not resolve the tick for this synthetic instrument or for another product, venue, jurisdiction, or effective date.
Implementation choiceThe canonical validator receives an already-resolved tick size and policy ID, then applies exact integer divisibility. It does not infer a regulatory tick from price alone.Frozen package definitionProduction control hierarchies, exemptions, overrides, and account/venue rules remain outside scope unless explicitly named.
Synthetic teaching inputCanonical orders, prices, thresholds, sessions, and identifiers are repository-authored.datasets/canonical-input.json and scenario-results.jsonThey are not observed participant or venue records.
Author-derived calculationThe synthetic price 1,000,500 atoms with a 100-atom tick divides exactly, so the order is accepted with zero remainder.Formula, canonical fixture, Python/TypeScript parity, and independent arithmeticCorrect arithmetic does not establish compliance, latency, or trading value.

The primary sources support only the named regulatory or venue behavior. They do not certify the synthetic policy IDs, orders, thresholds, sessions, or outputs. Those values are repository-authored, and every displayed result is an author-derived calculation under the selected control contract.

Formula, symbols, and numerical policy

Plain text
valid = (price_atoms mod tick_size_atoms) = 0
SymbolMeaningUnitPolicy
psubmitted integer priceatomspositive
τeffective tick sizeatomsresolved before validation
rdivision remainderatomsp mod τ
  • All price arithmetic is integer and exact.
  • The tick is supplied by a point-in-time reference service.
  • The package does not activate the delayed amended Rule 612 regime early.

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

  1. Validate price, tick, scale, and policy identity
  2. Divide price by tick using integer arithmetic
  3. Accept a zero remainder
  4. Otherwise report lower/upper valid neighbors and reject

Production-minded operational checklist

  1. Resolve instrument and policy date
  2. Load the effective tick and scale
  3. Validate with integer modulo
  4. Return neighboring prices and policy ID
  5. Retain the decision for audit

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, valid, is valid = true, remainder 0 atoms, with both valid neighbors equal to 1,000,500 atoms. The complete input and output are in datasets/canonical-input.json and datasets/expected-output.json.

The synthetic price 1,000,500 atoms with a 100-atom tick divides exactly, so the order is accepted with zero remainder.

Counterfactual checkpoint

Move 25 atoms off a 100-atom grid. Keep the policy and tick fixed, but submit 1,000,525 atoms. The output changes because Integer modulo changes from zero to 25; visual proximity cannot substitute for exact grid membership.

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.

ScenarioReview focusPurposeStatePrimary outputDiagnosticDecision segments
Canonical grid sweepStep 5 · canonical fixtureMove an integer-scaled price across the canonical 100-atom grid. Synthetic data; the effective policy remains explicit.acceptedremainder 0 atomson-grid; neighbors 1000500 / 100050025
Exact on-grid equalityStep 30 · comparison focusHold the effective tick fixed and land exactly on a valid grid point. Synthetic data; the effective policy remains explicit.acceptedremainder 0 atomson-grid; neighbors 1003000 / 10030001
Finer 50-atom gridStep 30 · comparison focusCompare the same price path under a finer point-in-time tick policy. Synthetic data; the effective policy remains explicit.acceptedremainder 0 atomson-grid; neighbors 1001500 / 10015001
Coarse-grid remainderStep 30 · comparison focusAdd 25 atoms to a 500-atom grid so nearby-looking prices remain invalid. Synthetic data; the effective policy remains explicit.rejectedremainder 25 atomsoff-grid; neighbors 1015000 / 10155001
Alternate 25-atom policyStep 30 · comparison focusShow how a smaller effective tick changes the set of valid prices. Synthetic data; the effective policy remains explicit.acceptedremainder 0 atomson-grid; neighbors 1000750 / 10007501
Policy-version comparisonStep 30 · comparison focusKeep prices deterministic while changing the effective grid identity and tick. Synthetic data; the effective policy remains explicit.acceptedremainder 0 atomson-grid; neighbors 1001500 / 10015001
Off-grid neighbor auditStep 30 · comparison focusReject a 25-atom remainder and expose both nearest valid prices. Synthetic data; the effective policy remains explicit.rejectedremainder 25 atomsoff-grid; neighbors 1003000 / 10031001

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

Tick-Size Validation 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 validate policy identity, price/quantity units, session or remembered state, and the supported mode before applying the control. Both return the decision together with distances, violations, cancellation/prevention events, or trigger state so an operator can reconstruct why the gate acted.

The main implementation branches are:

  • remainder = 0 — Accept price, because Exactly on effective grid.
  • remainder > 0 — Reject and report neighbors, because Off-grid price.
  • policy ID missing — Reject input, because Decision is not reproducible.

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:

  • A valid price has zero remainder.
  • The submitted price is between its reported neighbors.
  • Policy identity is retained with the decision.
  • The structured output retains valid, state, policy context, and reason fields.

Passing these checks proves that the deterministic reference matches the selected control contract. It does not certify exchange conformance, regulatory compliance, latency, operational resilience, or the safety of an override.

Failure modes and misuse

  • Passing one control does not imply an order passes every venue, broker, regulatory, credit, position, or market-access check.
  • Reference prices, bands, thresholds, group identifiers, and disconnect ownership must be point-in-time inputs; later values cannot repair an earlier decision.
  • A definition-correct control does not certify production latency, legal compliance, operational resilience, or trading profitability.

Debugging order

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

  1. Confirm instrument, venue/product, session, order type, side, and policy ID.
  2. Confirm integer price scale, quantity units, reference or band as-of time, and trigger clock.
  3. Confirm identity/ownership scope, mode, equality rule, threshold ordering, and remembered state.
  4. Recalculate the invariant and the declared scenario focus before changing code.

Evidence and historical boundary

Historical decision: deferred. A named production-control event would require complete point-in-time order, policy-version, reference-data, session, override, acknowledgement, and venue evidence plus redistribution permission. A labeled synthetic fixture is more reproducible and avoids implying a public record proves private control behavior.

The primary sources are SEC Rule 612 status. They support the source roles listed in the research ledger, not a redistributable historical observation, a private participant decision, current configuration at an unnamed venue, compliance certification, trading outcome, profitability claim, or prediction claim.

Summary and next topic

You can now validate point-in-time price grids without floating-point drift. The learning flow is: Volatility-Auction Reopening → Tick-Size Validation → Price-Band Validation. Carry the result forward only with its scope, clock, state, and evidence label.

Tick-Size Validation calculation flow

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

Rendering system map…

Takeaway: A valid price lands exactly on the effective grid; nearby-looking is not sufficient.

ReferencesPrimary sources and evidence notes

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

S1 — Statement Regarding Minimum Pricing Increments and Access Fee Caps

  • Organization or authors: U.S. Securities and Exchange Commission
  • Source type: Official regulator statement
  • Publication or effective date: 2026-06-11
  • Version: Current at build date
  • URL or DOI: https://www.sec.gov/newsroom/speeches-statements/atkins-statement-minimum-pricing-increments-access-fee-caps-061126
  • Accessed: 2026-07-30
  • Jurisdiction: United States NMS equities
  • Supports: The amended Rule 612 half-cent regime and the temporary compliance relief extending to the first business day of November 2027.
  • Limitations: Does not provide a universal tick for other jurisdictions, products, venues, or dates.

Evidence boundary

The sources establish only the current or historical rule and protocol facts named in each source record. They do not verify the repository-authored orders, policy identifiers, reference values, thresholds, session state, override authority, or output.

order-controls.ts
/* Deterministic reference algorithms for D12-F03 Order Controls. */

type Inputs = Record<string, any>;

function integer(name: string, value: unknown, positive = false, nonnegative = false): number {
  if (typeof value !== "number" || !Number.isInteger(value)) throw new Error(`${name} must be an integer`);
  if (positive && value <= 0) throw new Error(`${name} must be positive`);
  if (nonnegative && value < 0) throw new Error(`${name} must be nonnegative`);
  return value;
}

function text(name: string, value: unknown): string {
  if (typeof value !== "string" || !value.trim()) throw new Error(`${name} must be a nonempty string`);
  return value.trim();
}

function booleanValue(name: string, value: unknown): boolean {
  if (typeof value !== "boolean") throw new Error(`${name} must be boolean`);
  return value;
}

export function tickSizeValidation(
  price_atoms: unknown,
  tick_size_atoms: unknown,
  price_scale: unknown,
  effective_policy_id: unknown,
): Record<string, unknown> {
  const price = integer("price_atoms", price_atoms, true);
  const tick = integer("tick_size_atoms", tick_size_atoms, true);
  const scale = integer("price_scale", price_scale, true);
  const policyId = text("effective_policy_id", effective_policy_id);
  if (tick > price) throw new Error("tick_size_atoms cannot exceed price_atoms");
  const quotient = Math.floor(price / tick);
  const remainder = price % tick;
  const lower = quotient * tick;
  const upper = remainder === 0 ? lower : lower + tick;
  const valid = remainder === 0;
  return {
    effective_policy_id: policyId,
    price_atoms: price,
    tick_size_atoms: tick,
    price_scale: scale,
    valid,
    remainder_atoms: remainder,
    lower_valid_price_atoms: lower,
    upper_valid_price_atoms: upper,
    distance_to_lower_atoms: price - lower,
    distance_to_upper_atoms: upper - price,
    reason: valid ? "on-grid" : "off-grid",
    state: valid ? "accepted" : "rejected",
  };
}

export function priceBandValidation(
  side: unknown,
  limit_price_atoms: unknown,
  lower_band_atoms: unknown,
  upper_band_atoms: unknown,
  band_as_of_ns: unknown,
  inclusive: unknown = true,
): Record<string, unknown> {
  const orderSide = text("side", side).toLowerCase();
  if (!["buy", "sell"].includes(orderSide)) throw new Error("side must be buy or sell");
  const price = integer("limit_price_atoms", limit_price_atoms, true);
  const lower = integer("lower_band_atoms", lower_band_atoms, true);
  const upper = integer("upper_band_atoms", upper_band_atoms, true);
  const asOf = integer("band_as_of_ns", band_as_of_ns, false, true);
  const includeEdges = booleanValue("inclusive", inclusive);
  if (lower >= upper) throw new Error("lower_band_atoms must be less than upper_band_atoms");
  const valid = includeEdges ? lower <= price && price <= upper : lower < price && price < upper;
  let reason = "inside-band";
  let violation = 0;
  if (price < lower || (price === lower && !includeEdges)) {
    reason = "below-lower-band"; violation = lower - price;
  } else if (price > upper || (price === upper && !includeEdges)) {
    reason = "above-upper-band"; violation = price - upper;
  }
  return {
    side: orderSide, limit_price_atoms: price, lower_band_atoms: lower, upper_band_atoms: upper,
    band_as_of_ns: asOf, inclusive: includeEdges, valid,
    distance_from_lower_atoms: price - lower, distance_to_upper_atoms: upper - price,
    violation_atoms: violation, reason, state: valid ? "accepted" : "rejected",
  };
}

export function selfTradePrevention(incoming_order: unknown, resting_orders: unknown, mode: unknown): Record<string, unknown> {
  if (!incoming_order || typeof incoming_order !== "object" || Array.isArray(incoming_order)) throw new Error("incoming_order must be an object");
  if (!Array.isArray(resting_orders)) throw new Error("resting_orders must be an array");
  const incoming = incoming_order as Inputs;
  const selectedMode = text("mode", mode).toLowerCase();
  if (!["cancel_newest", "cancel_oldest", "decrement_both"].includes(selectedMode)) throw new Error("unsupported self-trade-prevention mode");
  const incomingId = text("incoming_order.order_id", incoming.order_id);
  const side = text("incoming_order.side", incoming.side).toLowerCase();
  if (!["buy", "sell"].includes(side)) throw new Error("incoming_order.side must be buy or sell");
  const price = integer("incoming_order.price_atoms", incoming.price_atoms, true);
  const quantity = integer("incoming_order.quantity", incoming.quantity, true);
  const participant = text("incoming_order.participant_id", incoming.participant_id);
  const group = text("incoming_order.stp_group", incoming.stp_group);
  const seen = new Set<string>([incomingId]);
  const parsed = resting_orders.map((raw: any, index: number) => {
    if (!raw || typeof raw !== "object" || Array.isArray(raw)) throw new Error(`resting_orders[${index}] must be an object`);
    const orderId = text(`resting_orders[${index}].order_id`, raw.order_id);
    if (seen.has(orderId)) throw new Error("order identifiers must be unique");
    seen.add(orderId);
    const restingSide = text(`resting_orders[${index}].side`, raw.side).toLowerCase();
    if (!["buy", "sell"].includes(restingSide) || restingSide === side) throw new Error("resting orders must be on the contra side");
    return {
      order_id: orderId, side: restingSide,
      price_atoms: integer(`resting_orders[${index}].price_atoms`, raw.price_atoms, true),
      quantity: integer(`resting_orders[${index}].quantity`, raw.quantity, true),
      participant_id: text(`resting_orders[${index}].participant_id`, raw.participant_id),
      stp_group: text(`resting_orders[${index}].stp_group`, raw.stp_group),
      sequence: integer(`resting_orders[${index}].sequence`, raw.sequence, false, true),
    };
  });
  parsed.sort((a, b) => side === "buy" ? a.price_atoms - b.price_atoms || a.sequence - b.sequence : b.price_atoms - a.price_atoms || a.sequence - b.sequence);
  let remaining = quantity;
  let externalExecuted = 0, prevented = 0, canceledIncoming = 0, canceledResting = 0;
  let stopped = false;
  const events: any[] = [], finalBook: any[] = [];
  for (const original of parsed) {
    const resting = { ...original };
    const marketable = side === "buy" ? resting.price_atoms <= price : resting.price_atoms >= price;
    if (stopped || remaining === 0 || !marketable) { finalBook.push(resting); continue; }
    const sameGroup = resting.participant_id === participant && resting.stp_group === group;
    const matchQty = Math.min(remaining, resting.quantity);
    if (sameGroup) {
      if (selectedMode === "cancel_newest") {
        canceledIncoming = remaining; prevented += matchQty;
        events.push({ action: "cancel-incoming", incoming_order_id: incomingId, resting_order_id: resting.order_id, prevented_quantity: matchQty });
        remaining = 0; stopped = true; finalBook.push(resting);
      } else if (selectedMode === "cancel_oldest") {
        canceledResting += resting.quantity; prevented += matchQty;
        events.push({ action: "cancel-resting", incoming_order_id: incomingId, resting_order_id: resting.order_id, prevented_quantity: matchQty });
      } else {
        resting.quantity -= matchQty; remaining -= matchQty; prevented += matchQty;
        events.push({ action: "decrement-both", incoming_order_id: incomingId, resting_order_id: resting.order_id, prevented_quantity: matchQty });
        if (resting.quantity > 0) finalBook.push(resting);
      }
    } else {
      resting.quantity -= matchQty; remaining -= matchQty; externalExecuted += matchQty;
      events.push({ action: "execute-external", incoming_order_id: incomingId, resting_order_id: resting.order_id, quantity: matchQty, price_atoms: resting.price_atoms });
      if (resting.quantity > 0) finalBook.push(resting);
    }
  }
  const state = prevented ? "self-trade-prevented" : remaining === 0 ? "externally-filled" : "resting-or-residual";
  return {
    mode: selectedMode, incoming_order_id: incomingId, original_incoming_quantity: quantity,
    external_executed_quantity: externalExecuted, prevented_self_quantity: prevented,
    canceled_incoming_quantity: canceledIncoming, canceled_resting_quantity: canceledResting,
    remaining_incoming_quantity: remaining, events, resting_orders: finalBook, state,
  };
}

export function cancelOnDisconnect(
  disconnected_session_id: unknown,
  disconnect_type: unknown,
  trigger_disconnect_types: unknown,
  policy: unknown,
  orders: unknown,
): Record<string, unknown> {
  const session = text("disconnected_session_id", disconnected_session_id);
  const eventType = text("disconnect_type", disconnect_type).toLowerCase();
  if (!Array.isArray(trigger_disconnect_types) || !trigger_disconnect_types.length) throw new Error("trigger_disconnect_types must be a nonempty array");
  const triggers = trigger_disconnect_types.map((item) => text("trigger_disconnect_type", item).toLowerCase());
  const selectedPolicy = text("policy", policy).toLowerCase();
  if (!["cancel_all", "cancel_continuous", "keep_gtc"].includes(selectedPolicy)) throw new Error("unsupported cancel-on-disconnect policy");
  if (!Array.isArray(orders)) throw new Error("orders must be an array");
  const seen = new Set<string>();
  const parsed = orders.map((raw: any, index: number) => {
    if (!raw || typeof raw !== "object" || Array.isArray(raw)) throw new Error(`orders[${index}] must be an object`);
    const orderId = text(`orders[${index}].order_id`, raw.order_id);
    if (seen.has(orderId)) throw new Error("order identifiers must be unique");
    seen.add(orderId);
    const book = text(`orders[${index}].book`, raw.book).toLowerCase();
    if (!["continuous", "auction"].includes(book)) throw new Error("book must be continuous or auction");
    return {
      order_id: orderId, session_id: text(`orders[${index}].session_id`, raw.session_id), book,
      time_in_force: text(`orders[${index}].time_in_force`, raw.time_in_force).toUpperCase(),
      quantity: integer(`orders[${index}].quantity`, raw.quantity, true),
    };
  });
  const triggered = triggers.includes(eventType);
  const canceled: string[] = [], retained: Array<{ order_id: string; reason: string }> = [];
  for (const order of parsed) {
    if (order.session_id !== session) { retained.push({ order_id: order.order_id, reason: "different-session" }); continue; }
    if (!triggered) { retained.push({ order_id: order.order_id, reason: "disconnect-type-not-configured" }); continue; }
    const shouldCancel = selectedPolicy === "cancel_all"
      || (selectedPolicy === "cancel_continuous" && order.book === "continuous")
      || (selectedPolicy === "keep_gtc" && order.time_in_force !== "GTC");
    if (shouldCancel) canceled.push(order.order_id);
    else retained.push({ order_id: order.order_id, reason: order.book === "auction" ? "auction-order-retained" : "gtc-retained" });
  }
  return {
    disconnected_session_id: session, disconnect_type: eventType, triggered, policy: selectedPolicy,
    canceled_order_ids: canceled, retained_orders: retained, canceled_count: canceled.length,
    retained_count: retained.length, state: triggered ? "purge-applied" : "no-purge",
  };
}

export function fatFingerLimit(
  side: unknown,
  limit_price_atoms: unknown,
  reference_price_atoms: unknown,
  quantity: unknown,
  max_quantity: unknown,
  max_notional_atoms: unknown,
  max_aggressive_deviation_bps: unknown,
): Record<string, unknown> {
  const orderSide = text("side", side).toLowerCase();
  if (!["buy", "sell"].includes(orderSide)) throw new Error("side must be buy or sell");
  const price = integer("limit_price_atoms", limit_price_atoms, true);
  const reference = integer("reference_price_atoms", reference_price_atoms, true);
  const qty = integer("quantity", quantity, true);
  const maxQty = integer("max_quantity", max_quantity, true);
  const maxNotional = integer("max_notional_atoms", max_notional_atoms, true);
  const maxDeviation = integer("max_aggressive_deviation_bps", max_aggressive_deviation_bps, false, true);
  const notional = price * qty;
  const signed = orderSide === "buy" ? price - reference : reference - price;
  const aggressiveDeviationBps = Math.max(0, Math.round((signed * 10000 / reference) * 1e6) / 1e6);
  const checks = {
    quantity: { value: qty, limit: maxQty, passed: qty <= maxQty },
    notional: { value: notional, limit: maxNotional, passed: notional <= maxNotional },
    aggressive_deviation_bps: { value: aggressiveDeviationBps, limit: maxDeviation, passed: aggressiveDeviationBps <= maxDeviation },
  };
  const violations = Object.entries(checks).filter(([, check]) => !check.passed).map(([name]) => name);
  return {
    side: orderSide, limit_price_atoms: price, reference_price_atoms: reference, quantity: qty,
    order_notional_atoms: notional, aggressive_deviation_bps: aggressiveDeviationBps,
    checks, violations, valid: violations.length === 0,
    reason: violations.length ? `limit-breached:${violations.join(",")}` : "within-configured-limits",
    state: violations.length ? "rejected" : "accepted",
  };
}

export function circuitBreakerTrigger(
  reference_close_atoms: unknown,
  current_index_atoms: unknown,
  level_thresholds_bps: unknown,
  previously_triggered_level: unknown = 0,
): Record<string, unknown> {
  const reference = integer("reference_close_atoms", reference_close_atoms, true);
  const current = integer("current_index_atoms", current_index_atoms, true);
  const previous = integer("previously_triggered_level", previously_triggered_level, false, true);
  if (previous > 3) throw new Error("previously_triggered_level cannot exceed 3");
  if (!Array.isArray(level_thresholds_bps) || level_thresholds_bps.length !== 3) throw new Error("level_thresholds_bps must contain exactly three thresholds");
  const thresholds = level_thresholds_bps.map((value) => integer("threshold_bps", value, true));
  if (new Set(thresholds).size !== 3 || thresholds.some((value, index) => index > 0 && value <= thresholds[index - 1])) throw new Error("thresholds must be strictly increasing");
  const declineBps = Math.max(0, Math.round(((reference - current) * 10000 / reference) * 1e6) / 1e6);
  let reached = 0;
  thresholds.forEach((threshold, index) => { if (declineBps >= threshold) reached = index + 1; });
  const newlyTriggered = reached > previous;
  const triggerLevel = newlyTriggered ? reached : 0;
  const actions = ["continue", "level-1-halt", "level-2-halt", "level-3-close"];
  const nextThreshold = reached < thresholds.length ? thresholds[reached] : null;
  const distance = nextThreshold === null ? null : Math.max(0, Math.round((nextThreshold - declineBps) * 1e6) / 1e6);
  return {
    reference_close_atoms: reference, current_index_atoms: current, decline_bps: declineBps,
    level_thresholds_bps: thresholds, previously_triggered_level: previous,
    reached_level: reached, newly_triggered_level: triggerLevel, newly_triggered: newlyTriggered,
    action: actions[triggerLevel], next_threshold_bps: nextThreshold,
    distance_to_next_threshold_bps: distance,
    state: newlyTriggered ? "triggered" : reached ? "already-triggered" : "normal",
  };
}

export function calculate(topicId: string, inputs: Inputs): Record<string, unknown> {
  if (!inputs || typeof inputs !== "object" || Array.isArray(inputs)) throw new Error("inputs must be an object");
  if (topicId === "D12-F03-A01") return tickSizeValidation(inputs.price_atoms, inputs.tick_size_atoms, inputs.price_scale, inputs.effective_policy_id);
  if (topicId === "D12-F03-A02") return priceBandValidation(inputs.side, inputs.limit_price_atoms, inputs.lower_band_atoms, inputs.upper_band_atoms, inputs.band_as_of_ns, inputs.inclusive);
  if (topicId === "D12-F03-A03") return selfTradePrevention(inputs.incoming_order, inputs.resting_orders, inputs.mode);
  if (topicId === "D12-F03-A04") return cancelOnDisconnect(inputs.disconnected_session_id, inputs.disconnect_type, inputs.trigger_disconnect_types, inputs.policy, inputs.orders);
  if (topicId === "D12-F03-A05") return fatFingerLimit(inputs.side, inputs.limit_price_atoms, inputs.reference_price_atoms, inputs.quantity, inputs.max_quantity, inputs.max_notional_atoms, inputs.max_aggressive_deviation_bps);
  if (topicId === "D12-F03-A06") return circuitBreakerTrigger(inputs.reference_close_atoms, inputs.current_index_atoms, inputs.level_thresholds_bps, inputs.previously_triggered_level);
  throw new Error(`unsupported topic_id: ${topicId}`);
}
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