---
title: "math-deduct-gold — 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/gold.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**

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# math-deduct-gold

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:** Postfix traversal memoizes ordered subtree keys, recursively obtains child ids, rejects child ids>255, normalizes +/* operand index order, emits a node and memoizes its new id. It returns None for0 or>8 operations; otherwise appends Stop. (bytes 17211–18746)
- **part of:** [math-deduct](https://md.groupants.elamur.ai/free/en/mova/math/src/deduct.rs.groupant/)
- **repository folder:** [`math/src/deduct.rs.groupant/gold.groupant`](https://github.com/ElamurAI/mova-free/tree/main/math/src/deduct.rs.groupant/gold.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) |
| `memo_key_asymmetry` | memo_key_asymmetry | partial source derived model | [memo_key_asymmetry](#memo-key-asymmetry) |
| `postfix_index_guard` | postfix_index_guard | partial source derived model | [postfix_index_guard](#postfix-index-guard) |

## Model text


### descriptant

#### math-deduct-gold

Postfix traversal memoizes ordered subtree keys, recursively obtains child ids, rejects child ids>255, normalizes +/* operand index order, emits a node and memoizes its new id. It returns None for0 or>8 operations; otherwise appends Stop.

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

Postfix traversal memoizes ordered subtree keys, recursively obtains child ids, rejects child ids>255, normalizes +/* operand index order, emits a node and memoizes its new id. It returns None for0 or>8 operations; otherwise appends Stop.

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

### invariant

#### Scoped domain and invariants

Accepted gold has1..8 arithmetic nodes plus final Stop. Caller must separately establish source leaf range and search candidate reachability.

##### Cost

Recursive key generation can revisit descendants at multiple ancestors; memo lookup and retained strings add work beyond one constant-time visit per tree node.

### models

### behavior_complement

A returned sequence cannot have more than8 Comb steps or an encoded child index>255. It can contain equal child ids and leaf ids>=n, so general validity/reachability cannot be inferred from success.

### reverse_reconstruction

Two occurrences of the identical (leaf0+leaf1) subtree collapse to one pool node. Swapping the children changes the memo key even though tkey canonicalizes the commutative tree; some equivalent arithmetic trees therefore have different memoization histories.

### memo_key_asymmetry

gold_steps' internal key preserves left/right order; tkey sorts Add/Mul child strings. Equality of tkey is weaker than equality of gold memo key.

### postfix_index_guard

A newly assigned node id may itself exceed255; rejection happens if a later parent attempts to use it. The checks constrain consumed operands, not all allocated pool ids.

### tests

#### Scoped evidence

Commutative tkey, reused identical subtree, leaf-only and operand256 rejection.

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

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.