---
title: "math-deduct — 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/"
---
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

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
- **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…`
- **repository folder:** [`math/src/deduct.rs.groupant`](https://github.com/ElamurAI/mova-free/tree/main/math/src/deduct.rs.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` |
| **composition** | partial | [composition](#composition) |
| **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) |
| `dag_reuse` | dag_reuse | partial source derived model | [dag_reuse](#dag-reuse) |
| `numeric_guard` | numeric_guard | partial source derived model | [numeric_guard](#numeric-guard) |
| `representation_transport` | representation_transport | partial source derived model | [representation_transport](#representation-transport) |
| `inference_training_state` | inference_training_state | partial source derived model | [inference_training_state](#inference-training-state) |

## Parts

- [math-deduct-transition](https://md.groupants.elamur.ai/free/en/mova/math/src/deduct.rs.groupant/transition.groupant/)
- [math-deduct-gold](https://md.groupants.elamur.ai/free/en/mova/math/src/deduct.rs.groupant/gold.groupant/)

## Model text


### descriptant

#### math-deduct

Reusable quantity-pool DAG search and postfix gold conversion.

Epoch 2026-10-31: source-derived partial model; prospective hypotheses retained before changes. Existing behavior unchanged except test helper path extraction. New bounded fixtures avoid annotated text/model/corpus/teacher paths. Child scopes use the parent syntax projection; lexical AST has no macro expansion or semantic resolution. Numeric thresholds and adapter differences are observations, not mathematical correctness proofs.

### approximant

#### Forward relation

Comb appends node retaining pool; Stop marks done. Candidate self-pairs absent, +/* only i<j. apply rejects zero divisor then nonfinite/negative/>1e12. Gold memoizes ordered subtree keys, normalizes commutative operand indices, allows1..8 operations and child indices<=255.

##### Domain

Valid pool/feature indices and finite scores assumed. Gold can emit self-combinations for repeated subtrees although search forbids them; gold acceptance is not reachability. u8 indices/uses and training clocks lack overflow certificates.

##### Executable approximant gap

No useful measured percentage surrogate is supplied for these categorical parse/search/effect observations. Supported future caps are 1%, 2%, 5%, 10% only, requiring an explicit metric and reference comparison. No speed or accuracy guarantee follows.

### invariant

#### Invariants and cost

Valid pool/feature indices and finite scores assumed. Gold can emit self-combinations for repeated subtrees although search forbids them; gold acceptance is not reachability. u8 indices/uses and training clocks lack overflow certificates.

##### Cost

Training constructor has three 2^22 arrays (~48MiB); averaged weights~16MiB. Precompute O(N²F); search O(S*B*(N+S)²) transitions times scoring/clone work and sorting.

Allocation failure, deep recursion, malformed public structures and universal numerical bounds are not verified.

### composition

#### Scoped composition

Reusable quantity-pool DAG search and postfix gold conversion.

Comb appends node retaining pool; Stop marks done. Candidate self-pairs absent, +/* only i<j. apply rejects zero divisor then nonfinite/negative/>1e12. Gold memoizes ordered subtree keys, normalizes commutative operand indices, allows1..8 operations and child indices<=255.

steps::Prob descriptions build Pre feature tables; gold_of maps Tree supervision into graph constraints and gold_steps. Search disallows self-pairs even where repeated gold subtree maps to same child id, so that join is partial.

### models

## Typed relations

### behavior_complement

Successful Comb excludes zero divisor and invalid/range-exceeding result. Gold rejects leaf-only or>8 operations; does not establish leaf index<n. beam0 training and huge pools unsupported.

### reverse_reconstruction

Canonical tkey admits swapped commutative children; final value admits many DAGs and weights. Memoized repeated subtrees hide repeated source tree occurrences.

### dag_reuse

Pool persists so previous intermediate values can be reused; self-pair gold/search mismatch remains explicit.

### numeric_guard

Result interval [0,1e12], finite; integrality tolerance1e-6 only applied at topk.

### representation_transport

tkey sorts commutative child strings, gold memo key does not; permuted equal trees need not share memo node.

### inference_training_state

averaged empties acc/stamp; inference use only, subsequent learn unsafe.

### tests

#### Source execution evidence

Safe command: cargo test -p math --lib wave28 -- --test-threads=1

Named outcomes (twice debug, twice release; sorted names equal; exits0):

```text
test deduct::wave28::dag_gold_reuses_subtrees_and_canonicalizes ... ok
test deduct::wave28::numeric_transition_boundary ... ok
```

One compiled assertion control for this source: compilation0, false expectation test101, exact byte restore, focused positive rerun0. These are actual source assertions, not copied implementations or semantic proof. Controls ran before rustfmt-only test-block formatting.

No dense Model allocation, beam/training/topk run; private apply/cands and gold conversion only. Gold self-pair/search mismatch documented without production change.

Strict math lib Clippy reports113 pre-existing production lints. No executable percentage surrogate, speed claim, model/corpus/teacher/GPU/full-school or held-out execution.