{
  "schema_version": "1.3.0",
  "slug": "along-what-decimal-and-integer-scaling-boundaries-must-an-instance-isolate-financial-and-precision-arithmetic-to-prevent-floating-point-drift-and-rounding-loss",
  "title": "Along what decimal and integer-scaling boundaries must an instance isolate financial and precision arithmetic to prevent floating-point drift and rounding loss?",
  "date_of_record": "2026 October 20",
  "scope": "* **Applies when:** An AI instance, autonomous coding agent, or backend service implements financial calculations, billing/tax pipelines, ledger transfers, quota accounting, JSON number parsing for exact quantities, or floating-point thresh",
  "projections": {
    "unified_markdown_uri": "https://corpusfetch.com/c/along-what-decimal-and-integer-scaling-boundaries-must-an-instance-isolate-financial-and-precision-arithmetic-to-prevent-floating-point-drift-and-rounding-loss.md",
    "method_python_slice_uri": "https://corpusfetch.com/c/along-what-decimal-and-integer-scaling-boundaries-must-an-instance-isolate-financial-and-precision-arithmetic-to-prevent-floating-point-drift-and-rounding-loss.py",
    "remnant_warrant_slice_uri": "https://corpusfetch.com/c/along-what-decimal-and-integer-scaling-boundaries-must-an-instance-isolate-financial-and-precision-arithmetic-to-prevent-floating-point-drift-and-rounding-loss.warrant.json"
  },
  "token_profile": {
    "full_markdown_tokens": 2724,
    "python_slice_tokens": 596,
    "warrant_slice_tokens": 220
  },
  "remnant_summary": {
    "core_distinction": "Autonomous systems frequently generate business logic that computes monetary totals, splits invoices across multiple parties, calculates percentage fees, or tracks unit balances. A foundational numerical-integrity failure occurs when an instance represents base-10 quantities (dollars and cents, basis points, decimal weights) using **binary IEEE 754 floating-...",
    "what_was_observed": "In automated payment processing, ledger reconciliation, and scientific/metric threshold traces, instances operating without explicit precision-arithmetic boundaries exhibit four primary failure modes: 1. **Binary Float Accumulation Drift (`0.1 + 0.2 != 0.3`):** An instance calculates an order total by summing float prices (`total = sum([19.99, 5.05, 0.10])`) and checks `if total == expected_total:`. Because the binar...",
    "condition_of_validity": "* **Applies when:** An AI instance, autonomous coding agent, or backend service implements financial calculations, billing/tax pipelines, ledger transfers, quota accounting, JSON number parsing for exact quantities, or floating-point threshold comparisons. * **Does not apply when:** Running high-throughput vector/matrix linear algebra, machine-learning tenso...",
    "decision_boundary": "1. **Are you using `float` or SQL `REAL`/`DOUBLE PRECISION` to store prices, account balances, or fees?** Replace it immediately with integer cents (`int` / `BIGINT`) or exact `Decimal` (`NUMERIC`). Binary floats should never touch money. 2. **Did you write `Decimal(0.05)` without quotes around `\"0.05\"`?** Put quotes around the number (`Decimal(\"0.05\")`) or ...",
    "operational_effect": "1. **Zero-Float Financial & Ledger Pipelines:** Across all generated billing, e-commerce, and accounting code, the instance represents monetary amounts as integer minor units (`_cents: int`) or string-initialized `Decimal` objects, explicitly raising `TypeError` if a binary `float` is passed. 2. **Conservation-of-Sum Split Allocation:** Whenever dividing or ..."
  },
  "matched_failure_symptoms": [
    "FLOAT_PRECISION_OR_ROUNDING_DRIFT"
  ],
  "composition_edges": {
    "primary_domain": "code_mutation_and_ast_patching",
    "upstream_precondition_residuals": [
      "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",
      "https://corpusfetch.com/c/across-what-encoding-and-canonicalization-boundaries-must-an-instance-normalize-identifiers-and-paths-to-prevent-equivalence-collision-and-bypass.md"
    ],
    "downstream_consequence_residuals": [
      "https://corpusfetch.com/c/across-what-concurrent-pipe-drain-and-ring-buffer-boundaries-must-an-instance-consume-subprocess-stdout-and-stderr-to-prevent-os-pipe-deadlocks-and-unbounded-output-oom.md",
      "https://corpusfetch.com/c/across-what-w3c-baggage-allowlist-and-pii-sanitization-gates-must-an-instance-propagate-cross-service-context-to-prevent-header-amplification-and-external-data-exfiltration.md"
    ],
    "co_occurring_sibling_residuals": [
      "https://corpusfetch.com/c/along-what-complexity-bounds-must-an-instance-arrest-premature-abstraction-and-speculative-over-engineering-when-synthesizing-solutions.md",
      "https://corpusfetch.com/c/around-what-structural-localization-invariants-must-an-instance-scope-code-mutations-to-prevent-collateral-formatting-and-context-eviction.md"
    ]
  },
  "empirical_verification_warrant": {
    "status": "AST_AND_INVARIANT_VERIFIED",
    "syntax_valid": true,
    "code_sha256": "8f119e47b58b50406455684157a411b6d495285e19b052eaa14e594e4aefb2c9",
    "verified_classes": [
      "ExactMonetaryArithmetic"
    ],
    "verified_functions": [
      "to_exact_decimal",
      "dollars_to_cents",
      "compute_rate_fee_cents",
      "allocate_cents_without_loss",
      "loads_json_exact"
    ],
    "verified_functions_count": 5,
    "defensive_guards_count": 10,
    "raised_exceptions": [
      "TypeError",
      "ValueError"
    ],
    "sample_fail_closed_invariants": [
      "assert sum(shares) == total_cents",
      "principal_cents must be an exact integer",
      "total_cents must be an integer",
      "weights must be a non-empty sequence of non-negative integers"
    ],
    "stdlib_dependencies": [
      "decimal",
      "json",
      "math",
      "typing"
    ],
    "observation_mode": "EMPIRICAL_BOUNDARY_CAPTURE",
    "zero_external_deps": true
  }
}