---
title: "math-deduct-transition — Mova code model"
description: "Mova code model of math/src/deduct.rs: components with their labels, obernants and the model text."
url: "https://groupants.elamur.ai/free/en/mova/math/src/deduct.rs.groupant/transition.groupant/"
---
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# math-deduct-transition

The groupant beside math/src/deduct.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/deduct.rs`](https://github.com/ElamurAI/mova-free/blob/main/math/src/deduct.rs)
- **source SHA-256:** `373e1e3d5d83d964…`
- **covers:** Comb clones state and appends Step, computes selected f64 operation, rejects zero divisor then nonfinite or outside[0,1e12], increments both operand uses and appends a node; Stop appends Step and marks done with pool unchanged. (bytes 8317–9527)
- **part of:** [math-deduct](https://md.groupants.elamur.ai/free/en/mova/math/src/deduct.rs.groupant/)
- **repository folder:** [`math/src/deduct.rs.groupant/transition.groupant`](https://github.com/ElamurAI/mova-free/tree/main/math/src/deduct.rs.groupant/transition.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) |
| `self_pair_boundary` | self_pair_boundary | partial source derived model | [self_pair_boundary](#self-pair-boundary) |
| `representative_selection` | representative_selection | partial source derived model | [representative_selection](#representative-selection) |

## Model text


### descriptant

#### math-deduct-transition

Comb clones state and appends Step, computes selected f64 operation, rejects zero divisor then nonfinite or outside[0,1e12], increments both operand uses and appends a node; Stop appends Step and marks done with pool unchanged.

Epoch 2026-10-31: replaced duplicate catalog sentences with concrete exclusions, compatible-antecedent examples and two distinct scoped behavioral views. Source and prior execution evidence are unchanged; this revision ran no tests.

### approximant

#### Scoped forward relation

Comb clones state and appends Step, computes selected f64 operation, rejects zero divisor then nonfinite or outside[0,1e12], increments both operand uses and appends a node; Stop appends Step and marks done with pool unchanged.

This source-derived relation is partial; no executable percentage surrogate or replacement is supplied.

### invariant

#### Scoped domain and invariants

Valid operand/feature indices and bounded uses counters are required. Old pool nodes remain and pool grows exactly1 on successful Comb; Stop retains pool size.

##### Cost

Every attempt clones pool/tree state before numerical rejection. Accepted Comb additionally clones operand trees and builds canonical key strings; rejected arithmetic is not allocation-free.

### models

### behavior_complement

Successful Comb cannot contain a new negative, nonfinite or>1e12 value under valid indices. Stop cannot append a numeric node. apply does not exclude equal operand indices even though cands does.

### reverse_reconstruction

Last value5 is compatible with8-3 or10/2, so the scalar cannot identify operands. Full resulting state plus its last Step preserves original pool and selected indices, narrowing reconstruction; use counters may still require bounded/no-overflow assumptions.

### self_pair_boundary

apply(Comb(i,i,Mul)) can succeed and increments that node's uses twice. cands enumerates only i!=j; gold acceptance and direct apply success therefore do not establish search reachability.

### representative_selection

New representative=a.rep when a is a leaf and b is not; otherwise b.rep. This differs from steps' max-text-index representative and affects feature transport.

### tests

#### Scoped evidence

Private actual apply/cands: divide0, negative, upper bound, legal difference, no candidate self-pair and Stop availability.

Named actual source fixtures: deduct::wave28::{numeric_transition_boundary}.

Parent tests.md records commands and paired profiles. No additional coverage inferred from parent fixtures outside this byte range; source-scoped numeric/parse properties remain partial.