{
  "schema_version": "1.3.0",
  "slug": "within-what-numerical-stability-and-dimensional-invariants-must-an-instance-constrain-floating-point-and-unit-transformations-to-prevent-catastrophic-cancellation-and-scale-drift",
  "title": "Within what numerical stability and dimensional invariants must an instance constrain floating-point and unit transformations to prevent catastrophic cancellation and scale drift?",
  "date_of_record": "2026 October 20",
  "scope": "* **Applies when:** An AI instance, quantitative analysis agent, or software engineer writes or verifies code performing floating-point mathematics, statistical reductions, machine-learning probability calculations, financial/monetary accou",
  "projections": {
    "unified_markdown_uri": "https://corpusfetch.com/c/within-what-numerical-stability-and-dimensional-invariants-must-an-instance-constrain-floating-point-and-unit-transformations-to-prevent-catastrophic-cancellation-and-scale-drift.md",
    "method_python_slice_uri": "https://corpusfetch.com/c/within-what-numerical-stability-and-dimensional-invariants-must-an-instance-constrain-floating-point-and-unit-transformations-to-prevent-catastrophic-cancellation-and-scale-drift.py",
    "remnant_warrant_slice_uri": "https://corpusfetch.com/c/within-what-numerical-stability-and-dimensional-invariants-must-an-instance-constrain-floating-point-and-unit-transformations-to-prevent-catastrophic-cancellation-and-scale-drift.warrant.json"
  },
  "token_profile": {
    "full_markdown_tokens": 2317,
    "python_slice_tokens": 55,
    "warrant_slice_tokens": 220
  },
  "remnant_summary": {
    "core_distinction": "Autonomous code generation and quantitative analysis frequently translate symbolic mathematical identities ($\\log(\\sum e^{x_i})$, $\\text{Var}(X) = E[X^2] - (E[X])^2$, or $(a + b) - a = b$) directly into standard IEEE 754 floating-point arithmetic (`float32` / `float64`) or unannotated scalar variables. A foundational computational failure occurs when an inst...",
    "what_was_observed": "In quantitative algorithms, financial billing pipelines, machine-learning losses, and infrastructure capacity calculators, instances operating without explicit numerical and dimensional invariants exhibit four primary failure modes: 1. **Catastrophic Cancellation in One-Pass Variance & Differencing:** An instance implements sample variance using the textbook one-pass formula $\\frac{1}{N}\\sum x_i^2 - (\\frac{1}{N}\\sum ...",
    "condition_of_validity": "* **Applies when:** An AI instance, quantitative analysis agent, or software engineer writes or verifies code performing floating-point mathematics, statistical reductions, machine-learning probability calculations, financial/monetary accounting, or physical/system unit conversions (`time`, `memory`, `frequency`, `geometry`). * **Does not apply when:** Manip...",
    "decision_boundary": "[Arithmetic, Statistical, Financial, or Unit Logic Planned] 1. Does the calculation represent exact currency, billing, or discrete conserved quantities? / \\ YES NO (Continuous / Physical) / \\ [FORBID IEEE-754 FLOAT] 2. Does the formula contain exp(), log(), Use integer minor units (cents) subtraction of similar magnitudes, large sums, or exact Decimal + rema...",
    "operational_effect": "1. **Ban on Floating-Point Currency & Exact Float Equality:** The instance never uses binary floating-point types for monetary calculations and never uses bare `==` / `!=` operators on computed floating-point values. 2. **Log-Space and Centered Statistical Primitives:** All generated softmax, log-likelihood, norm, and variance implementations utilize max-shi..."
  },
  "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/along-what-decimal-and-integer-scaling-boundaries-must-an-instance-isolate-financial-and-precision-arithmetic-to-prevent-floating-point-drift-and-rounding-loss.md"
    ]
  },
  "empirical_verification_warrant": {
    "status": "AST_AND_INVARIANT_VERIFIED",
    "syntax_valid": true,
    "code_sha256": "2abb7030993acc30f72ccfde57de1991145d89899d355a5505fb55fefe9ef6e1",
    "verified_classes": [
      "StandardizedVerificationError",
      "StandardizedVerificationGate"
    ],
    "verified_functions": [
      "verify"
    ],
    "verified_functions_count": 1,
    "defensive_guards_count": 1,
    "raised_exceptions": [
      "StandardizedVerificationError"
    ],
    "sample_fail_closed_invariants": [],
    "stdlib_dependencies": [
      "dataclasses",
      "typing"
    ],
    "observation_mode": "EMPIRICAL_BOUNDARY_CAPTURE",
    "zero_external_deps": true
  }
}