Source: https://guthlabs.ai/docs/instruments/prime-factorization-divisor-explorer/implementation/

instrument implementation / implementation-contract

# Prime Factorization & Divisor Explorer implementation

A source-bound implementation contract for Prime Factorization & Divisor Explorer; 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**: t6-046

**Effect**: Computation or source lookup only

## Input and validation requirements

- Reject zero, negative values, nonintegers, and non-finite inputs; n=0 has infinitely many divisors and would make the requested functions undefined.

- A divisor-count or divisor-sum implementation that uses ordinary JavaScript Number values can silently lose precision for integers above 2^53−1.

- Trial division can be impractically slow for large semiprimes; Pollard's rho can also require unbounded retries and needs a correct primality test and factor-completion logic.

- Pollard's rho is commonly randomized; an unseeded random implementation is not reproducible, so deterministic testing requires a specified seed or deterministic test properties.

- Generating the complete divisor list can require substantial memory even when factorization itself is fast.

- Classification requires computing or comparing σ(n) against 2n exactly, not using floating-point arithmetic.

## 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": {
    "n": 1
  },
  "expected_outputs": {
    "factorization": "1",
    "divisors": [
      "1"
    ],
    "divisor_count": "1",
    "divisor_sum": "1",
    "proper_divisor_sum": "0",
    "classification": "deficient"
  },
  "working": "1 has no prime factors. Its positive divisor list is [1]. Therefore d(1)=1 and σ(1)=1. The proper-divisor sum is σ(1)-1=1-1=0. Since 0<1, 1 is deficient."
}
````

## Other records

[01**Overview**](<https://guthlabs.ai/docs/instruments/prime-factorization-divisor-explorer/>)[02**Mechanism**](<https://guthlabs.ai/docs/instruments/prime-factorization-divisor-explorer/mechanism/>)[04**Qualification**](<https://guthlabs.ai/docs/instruments/prime-factorization-divisor-explorer/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-tranche6/tranche6-results.json`