---
title: "math-nt-factor — Mova code model"
description: "Mova code model of math/src/nt.rs: components with their labels, obernants and the model text."
url: "https://groupants.elamur.ai/free/en/mova/math/src/nt.rs.groupant/factor.groupant/"
---
Elamur: [Mova](https://md.mova.elamur.ai/free/en/) · [Dictionary](https://md.dictionary.elamur.ai/free/en/) · [Research](https://md.research.elamur.ai/free/en/) · **Groupants**

This page as HTML: <https://groupants.elamur.ai/free/en/mova/math/src/nt.rs.groupant/factor.groupant/>

# math-nt-factor

The groupant beside math/src/nt.rs in the Mova repository: what the code computes, what it never does, how to go back from its outputs, its invariants, cost and checks.

## Facts

- **kind:** groupant_fragment
- **status:** partial source bound model
- **source:** [`math/src/nt.rs`](https://github.com/ElamurAI/mova-free/blob/main/math/src/nt.rs)
- **source SHA-256:** `27f4bf91578ab245…`
- **covers:** Fixed-base MR, recursive Pocklington and Pollard split magnitudes. Probable factors count complete. Sorted factors preserve product under producer domain, except zero's empty convention. Budget/deadline checks do not bound all work. No randomized-error claim follows from fixed bases. (bytes 5534–18019)
- **part of:** [math-nt](https://md.groupants.elamur.ai/free/en/mova/math/src/nt.rs.groupant/)
- **repository folder:** [`math/src/nt.rs.groupant/factor.groupant`](https://github.com/ElamurAI/mova-free/tree/main/math/src/nt.rs.groupant/factor.groupant)
- **repository commit:** `48f2e6f74146`

> **Implementation material.** A Mova code model describes this code at one source revision: partial models, finite checks and their stated scope. It is not a reviewed general exposition, and its labels are shown as written, never raised.

## Components

| component | label | where |
|---|---|---|
| **approximant** | partial | [approximant](#approximant) |
| **ast** | partial | `../syntax.json` |
| **descriptant** | present | [descriptant](#descriptant) |
| **invariant** | partial | [invariant](#invariant) |
| **tests** | executed bounded checks | [tests](#tests) |

## Obernants

The typed relations around the forward model: the behaviour complement (what the code never does), the reverse reconstruction (every input compatible with an output) and specialised views.

| id | type | label | where |
|---|---|---|---|
| `behavior_complement` | behavior_complement | partial source derived model | [behavior_complement](#behavior-complement) |
| `reverse_reconstruction` | reverse_reconstruction | partial source derived model | [reverse_reconstruction](#reverse-reconstruction) |
| `primality_classes` | primality_classes | partial source derived model | [primality_classes](#primality-classes) |
| `pocklington_condition` | pocklington_condition | partial source derived model | [pocklington_condition](#pocklington-condition) |
| `budget_effect` | budget_effect | partial source derived model | [budget_effect](#budget-effect) |
| `factor_certificate` | factor_certificate | partial source derived model | [factor_certificate](#factor-certificate) |

## Model text


### descriptant

#### math-nt-factor

Fixed-base MR, recursive Pocklington and Pollard split magnitudes. Probable factors count complete. Sorted factors preserve product under producer domain, except zero's empty convention. Budget/deadline checks do not bound all work. No randomized-error claim follows from fixed bases.

Epoch 2026-10-31: complete source read, parent AST reused; partial finite evidence only.

### approximant

#### Scoped forward and cost

Fixed-base MR, recursive Pocklington and Pollard split magnitudes. Probable factors count complete. Sorted factors preserve product under producer domain, except zero's empty convention. Budget/deadline checks do not bound all work. No randomized-error claim follows from fixed bases.

No executable percent surrogate claimed.

### invariant

#### Scoped invariant

Fixed-base MR, recursive Pocklington and Pollard split magnitudes. Probable factors count complete. Sorted factors preserve product under producer domain, except zero's empty convention. Budget/deadline checks do not bound all work. No randomized-error claim follows from fixed bases.

Source range[5396,17881) bound by manifest digest. Parent domain applies, not arbitrary public states.

### models

## Source-scoped typed relations

### behavior_complement

A composite unresolved by Pollard excludes complete=true, but Probable factor does not. Negative n excludes negative factor entries because magnitude is factored.

### reverse_reconstruction

Nonempty factors reconstruct |n| as product p^e, losing sign. Empty producer factors admit n=0,1,-1. Sorted merged factors lose split/trial traversal history and time/budget usage.

### primality_classes

u64 uses12 fixed prime bases. Larger inputs try small primes,30 fixed bases, depth-limited Pocklington, then Probable. Fixed bases do not justify a randomized4^-30 error statement.

### pocklington_condition

Accumulate only proven prime factors of n-1 into F; require F²>n and for each q a<200 with a^(n-1)=1 and gcd(a^((n-1)/q)-1,n)=1. Failure to find witnesses returns no certificate.

### budget_effect

Pollard decrements budget in blocks; trial/primality, initial doubling and recovery omit the check. u64 ignores deadline; big checks deadline only within blocks. A budget is not total arithmetic work.

### factor_certificate

check_factor multiplies powers and requires complete plus prime-like factors; zero with empty list is specially accepted. It repeats probable acceptance and cannot convert that status to proven prime.

### tests

#### Evidence

See ../tests.md for actual checks and source mutant; this fragment adds no runtime test.

Fixed-base MR, recursive Pocklington and Pollard split magnitudes. Probable factors count complete. Sorted factors preserve product under producer domain, except zero's empty convention. Budget/deadline checks do not bound all work. No randomized-error claim follows from fixed bases.