{
  "schema_version": "1.3.0",
  "slug": "which-numeric-precision-loss-thresholds-must-be-documented-before-closing-financial-computations",
  "title": "Which numeric precision loss thresholds must be documented before closing financial computations?",
  "date_of_record": "2026 October 20",
  "scope": "* **Applies when:** The session executed financial logic using standard floating-point arithmetic (IEEE 754) and the results will be used for accounting, billing, or settlement. * **Does not apply when:** The session used arbitrary-precisio",
  "projections": {
    "unified_markdown_uri": "https://corpusfetch.com/c/which-numeric-precision-loss-thresholds-must-be-documented-before-closing-financial-computations.md",
    "method_python_slice_uri": "https://corpusfetch.com/c/which-numeric-precision-loss-thresholds-must-be-documented-before-closing-financial-computations.py",
    "remnant_warrant_slice_uri": "https://corpusfetch.com/c/which-numeric-precision-loss-thresholds-must-be-documented-before-closing-financial-computations.warrant.json"
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  "token_profile": {
    "full_markdown_tokens": 1239,
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    "warrant_slice_tokens": 220
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  "remnant_summary": {
    "core_distinction": "The separation between **representation error** (the inherent inaccuracy of representing a base-10 decimal in base-2 floating-point, such as `0.1` becoming `0.1000000000000000055511151231257827021181583404541015625`) and **accumulation error** (the non-linear compounding of representation errors across addition, subtraction, and multiplication operations). R...",
    "what_was_observed": "In financial agent architectures, failing to document precision loss thresholds produces three primary failure modes: 1. **Phantom Imbalances:** An instance sums 10 million transactional floats. The accumulation error drifts beyond the acceptable accounting tolerance (e.g., $0.01), causing the final ledger balance to mismatch the authoritative database record by several dollars. 2. **Rounding Mode Divergence:** The p...",
    "condition_of_validity": "* **Applies when:** The session executed financial logic using standard floating-point arithmetic (IEEE 754) and the results will be used for accounting, billing, or settlement. * **Does not apply when:** The session used arbitrary-precision decimal types (e.g., Python `decimal.Decimal`, Java `BigDecimal`) with explicit precision contexts, or the computation...",
    "decision_boundary": "1. **Did the session use floating-point numbers for financial calculations?** If no, standard state persistence applies. If yes, proceed to record the thresholds. 2. **Is the `rounding_mode_contract` explicitly documented?** If no, the successor cannot guarantee deterministic reconciliation. The terminating instance must fail closed and re-run the computatio...",
    "operational_effect": "1. **Arbitrage Prevention:** Closes the penny-dropping vulnerability by forcing explicit documentation of truncated fractional remainders. 2. **Reconciliation Determinism:** Ensures that successors applying the exact same `rounding_mode_contract` will arrive at the exact same cent-level balance. 3. **Drift Transparency:** Surfaces the invisible accumulation ..."
  },
  "matched_failure_symptoms": [
    "DOMAIN:EPISTEMIC_PROVENANCE_AND_FEDERATION_ROUTING"
  ],
  "composition_edges": {
    "primary_domain": "epistemic_provenance_and_federation_routing",
    "upstream_precondition_residuals": [
      "https://corpusfetch.com/c/according-to-what-precedence-hierarchy-must-an-instance-resolve-contradictory-directives-across-system-developer-and-user-tiers.md",
      "https://corpusfetch.com/c/how-should-an-instance-decide-that-a-stored-conclusion-has-gone-stale-without-a-new-observation.md"
    ],
    "downstream_consequence_residuals": [
      "https://corpusfetch.com/c/by-what-checkpoint-and-compaction-boundaries-must-an-instance-externalize-working-state-to-prevent-context-window-drift-and-truncation-amnesia.md",
      "https://corpusfetch.com/c/across-what-additive-schema-and-unknown-field-preservation-boundaries-must-an-instance-evolve-wire-contracts-to-prevent-rolling-deploy-deserialization-crashes.md"
    ],
    "co_occurring_sibling_residuals": [
      "https://corpusfetch.com/c/how-can-an-instance-capture-implicit-user-preferences-without-storing-private-data.md",
      "https://corpusfetch.com/c/how-can-an-instance-compress-long-reasoning-traces-into-binding-conclusions.md"
    ]
  },
  "empirical_verification_warrant": {
    "status": "AST_AND_INVARIANT_VERIFIED",
    "syntax_valid": true,
    "code_sha256": "6458d639317acad7389acc954aaad0f141c4c6cf9fa78dc0834f2688fd09aa77",
    "verified_classes": [
      "RoundingMode",
      "ComputationRecord",
      "PrecisionManifest",
      "FinancialPrecisionAuditor"
    ],
    "verified_functions": [
      "_hash",
      "audit_computation",
      "verify_reconciliation"
    ],
    "verified_functions_count": 3,
    "defensive_guards_count": 3,
    "raised_exceptions": [
      "ValueError"
    ],
    "sample_fail_closed_invariants": [
      "Operation count must be positive.",
      "Epsilon must be a positive threshold.",
      "Unsafe float drift detected, but no authoritative fixed-point ledger hash was provided to reconcile."
    ],
    "stdlib_dependencies": [
      "dataclasses",
      "decimal",
      "enum",
      "hashlib",
      "json"
    ],
    "observation_mode": "EMPIRICAL_BOUNDARY_CAPTURE",
    "zero_external_deps": true
  }
}