Source: https://guthlabs.ai/docs/instruments/big-number-arbitrary-precision-calculator/mechanism/

instrument mechanism / verified-clean

# Big Number / Arbitrary Precision Calculator mechanism

The inspectable method record for Big Number / Arbitrary Precision Calculator, kept separate from implementation and qualification.

Status: **VERIFIED_CLEAN**Lifecycle: **verified-clean**

## Model scope

The core idea—arbitrary-size integer arithmetic using BigInt and decimal arithmetic using a correctly configured arbitrary-precision decimal library—is standard. However, the specification is incomplete for decimal precision and rounding, division, expression syntax, and factorial domain constraints, so the instrument cannot be verified as fully correct without those definitions.

- BigInt arithmetic is exact for integers, but BigDecimal arithmetic is not fully specified: decimal precision, rounding mode, scale handling, and representation of non-terminating division results are missing.

- The expression grammar and operator semantics are unspecified, including exponent constraints, factorial syntax, precedence, and whether integer division truncates or produces a decimal.

- Factorial support needs an explicit domain constraint: n must be a non-negative integer; negative and non-integer factorial inputs are invalid unless Gamma-function semantics are intentionally supported.

- The label 'exact large-integer or high-precision decimal result' is ambiguous for decimal division and other non-terminating results; the output is only exact when the result terminates or when an exact rational representation is supported.

## Units and conventions

- All inputs are dimensionless mathematical quantities; no physical units or unit conversion are performed.

- Integer literals are interpreted in base 10 and represented exactly with arbitrary-size signed integers.

- Decimal literals are interpreted as base-10 decimal values. Exactness is assumed for terminating decimal operations in these test vectors; non-terminating results require a specified precision and rounding policy.

- Exponentiation in the test vectors uses a non-negative integer exponent and exact integer arithmetic.

## Inspectable vector

One of 4 source-bound review vectors:

````
{
  "inputs": {
    "expression": "0!",
    "domain": "factorial"
  },
  "expected_outputs": {
    "result": "1",
    "type": "exact_integer"
  },
  "reference_data": {
    "identity": "0!=1",
    "algorithm": "factorial(n)=1*2*...*n with the empty product defined as 1"
  },
  "working": "0! is the empty product. By definition, 0!=1."
}
````

## Failure boundary

**BREAK_CLAIMED** · SELF_FLAGGED

The specification does not define division-by-zero behavior or unary-minus versus exponentiation precedence. An implementation can therefore produce an invalid non-error result for 1 / 0 or disagree on the value of -3^2, despite supporting arbitrary precision.

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/big-number-arbitrary-precision-calculator/>)[03**Implementation**](<https://guthlabs.ai/docs/instruments/big-number-arbitrary-precision-calculator/implementation/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/big-number-arbitrary-precision-calculator/qualification/>)

## Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

- `VERIFIED_LEDGER.json`

- `evidence-tranche8/tranche8-results.json`

- `BOUNDARY_HAZARD_CATALOG.json`