Source: https://guthlabs.ai/docs/instruments/big-integer-base-n-arithmetic/implementation/

instrument implementation / implementation-contract

# Big Integer Base-N Arithmetic implementation

A source-bound implementation contract for Big Integer Base-N Arithmetic; deployment and executable qualification remain separate.

Status: **VERIFIED_CLEAN**Lifecycle: **implementation-contract**

## Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

**Record owner**: Guth Instruments

**Lifecycle**: verified-clean

**Evidence ID**: t5-004

**Effect**: Computation or source lookup only

## Input and validation requirements

- Division by zero must be rejected before any division step.

- Invalid digits, a base below 2, noninteger bases, and mismatched operand bases must be rejected.

- If negative integers are supported, sign normalization and subtraction cases such as a smaller minuend must be explicitly defined and tested.

- A JavaScript Number used for intermediate digit products or carry accumulation can lose precision; arbitrary precision requires BigInt or carefully bounded digit arithmetic.

- Malformed inputs, empty digit arrays, leading signs, leading zeros, and zero normalization need explicit validation rules.

- The division output must state whether it is quotient-only or quotient-plus-remainder and must define behavior for negative operands.

- The empty honest_label field is a labeling concern: the catalog should not imply fully verified arbitrary-precision support until base validation, signed arithmetic, division semantics, and precision guarantees are specified and tested.

## Required corrections

No binding erratum is attached to this unique-name record. Implementers must still preserve the declared units, domain, and failure behavior.

## Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

````
{
  "inputs": {
    "base": 16,
    "left": "FFFF",
    "right": "1",
    "operation": "add"
  },
  "expected_outputs": {
    "result": "10000",
    "carry_borrow_trace": {
      "carry_out_by_position": [
        1,
        1,
        1,
        1
      ],
      "final_carry": 1
    }
  },
  "working": "Process right to left: F + 1 = 16, write 0 and carry 1; F + 0 + 1 = 16, write 0 and carry 1; F + 0 + 1 = 16, write 0 and carry 1; F + 0 + 1 = 16, write 0 and carry 1. Append the final carry 1. Result = 10000 base 16."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/big-integer-base-n-arithmetic/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/big-integer-base-n-arithmetic/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/big-integer-base-n-arithmetic/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-tranche5/tranche5-results.json`