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

The groupant beside math/src/understand.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/understand.rs`](https://github.com/ElamurAI/mova-free/blob/main/math/src/understand.rs)
- **source SHA-256:** `5b3ac990c5e46e75…`
- **repository folder:** [`math/src/understand.rs.groupant`](https://github.com/ElamurAI/mova-free/tree/main/math/src/understand.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) |
| `placeholder_transport` | placeholder_transport | partial source derived model | [placeholder_transport](#placeholder-transport) |
| `failure_precedence` | failure_precedence | partial source derived model | [failure_precedence](#failure-precedence) |
| `unit_semantics` | unit_semantics | partial source derived model | [unit_semantics](#unit-semantics) |
| `operator_associativity` | operator_associativity | partial source derived model | [operator_associativity](#operator-associativity) |

## Parts

- [math-understand-chunk](https://md.groupants.elamur.ai/free/en/mova/math/src/understand.rs.groupant/chunk.groupant/)
- [math-understand-frames](https://md.groupants.elamur.ai/free/en/mova/math/src/understand.rs.groupant/frames.groupant/)
- [math-understand-pratt](https://md.groupants.elamur.ai/free/en/mova/math/src/understand.rs.groupant/pratt.groupant/)

## Model text


### descriptant

#### math-understand

Dictionary chunks, parser placeholder transport and ordered arithmetic frames.

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

chunk prefers number then unit then word; standins preserve owner index but erase sign/unit details. parse_sentence maps heads, tree cases then fallback, conditions and deltas. Interp rejects unknown before absent numbers, then chance/percent/comparison/state/source/conversion. Pratt precedence1/2/3/4, power right-associative.

##### Domain

Valid annotation heads and nonempty Interp sentences assumed. Bare conversion target cannot supply default source scale. Rat parse errors may become unknown words. No teacher calls; annotation/model paths unexecuted.

##### 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 annotation heads and nonempty Interp sentences assumed. Bare conversion target cannot supply default source scale. Rat parse errors may become unknown words. No teacher calls; annotation/model paths unexecuted.

##### Cost

Token progression plus Rat/lookup work; repeated item/placeholder scans and subtree membership can be cubic; Pratt linear with nesting-depth recursion. Annotation separate.

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

### composition

#### Scoped composition

Dictionary chunks, parser placeholder transport and ordered arithmetic frames.

chunk prefers number then unit then word; standins preserve owner index but erase sign/unit details. parse_sentence maps heads, tree cases then fallback, conditions and deltas. Interp rejects unknown before absent numbers, then chance/percent/comparison/state/source/conversion. Pratt precedence1/2/3/4, power right-associative.

lex lookup and units/Rat produce chunks; parser standins return mapped roles; ordered frames/Pratt produce Expr, which eval validates separately. Private helper tests bypass actual Annotator and cannot establish English quality.

### models

## Typed relations

### behavior_complement

Unknown alphabetic token excludes success before quantity/frame gates. Missing scale and malformed fraction/parentheses reject. Helper success does not certify English parse or dimensional evaluation.

### reverse_reconstruction

Many synonyms and parentheses lead to same Expr. standins cannot recover sign/unit/exact fraction without original Items; decimal fallback7 is lossy.

### placeholder_transport

Quantity unit creates two tokens; fractions become half, sign removed, decimal failure uses7; owner index maps back to retained Item.

### failure_precedence

Unknown-word gate before quantity and frames; chance preempts other triggers.

### unit_semantics

Scale->Temp for absolute, delta->Qty(delta unit); Degrees requires explicit quantity scale, never bare target.

### operator_associativity

Unary parses before power; nonpercent lhs +/- percent rhs rewrites lhs*(1 +/- rhs); slash fraction of multiplies.

### 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 understand::wave28::chunk_units_and_placeholder_transport ... ok
test understand::wave28::pratt_precedence_and_percent_rewrite ... ok
test understand::wave28::rejection_precedence_and_scale_ambiguity ... 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 model load or parse_sentence; actual chunk/standins/Interp/Pratt helpers with synthetic tokens. English frames and annotation mapping remain partial.

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.