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

# math-orchestration

The groupant beside models/math-orchestration.groupant 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_group
- **status:** partial descriptive instance
- **bound sources:** 14
- **repository folder:** [`models/math-orchestration.groupant`](https://github.com/ElamurAI/mova-free/tree/main/models/math-orchestration.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 | [forward](#forward) |
| **ast** | not materialized |  |
| **composition** | partial | [composition](#composition) |
| **cost** | symbolic source derived | [cost](#cost) |
| **descriptant** | present | [descriptant](#descriptant) |
| **invariant** | partial | [invariant](#invariant) |
| **tests** | see source local evidence | [checks](#checks) |

## 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) |
| `expectation-join` | representation_transport | partial source derived model | [expectation-join](#expectation-join) |
| `fallback-state` | state_transition | partial source derived model | [fallback-state](#fallback-state) |
| `effect-order` | failure_precedence | partial source derived model | [effect-order](#effect-order) |
| `budget-composition` | resource_boundary | partial source derived model | [budget-composition](#budget-composition) |

## Model text


### descriptant

#### math-orchestration: wave28

Problem kind/source→Expect integer/options→gate; plan/curriculum normalizers and tolerances differ. Template substitution lossy then gate rechecks. CLI held policy outside run_c. Vmm cap precheck not reservation. Build output enters lex module; suite uses separate small-unit engine.

This source-bound partial group organizes existing Mova code. Native evidence and excluded effects are recorded in source sidecars and the root wave28 report. Registration is not a universal proof or whole-system runtime claim.

### model

## math-orchestration

### forward

Problem→Expect→Plan→Trace; verified=fails.empty&&answer.Some. B.correct=verified&&grade. Verified B→Memo regardless correct; C tries<=3 compatible templates then gates else copies B fields. CLI selects data/effect routes; Vmm/Lean explicit external boundaries.

### invariant

Verification distinct from gold correctness. C fallback keeps by_slm=false. Strict over-cap and forbidden-proof preflight exclude corresponding call effects only under actual early return guards.

### cost

Sampling O(n log n), delegated arithmetic/enumeration, perceptron training and bounded template attempts; teacher retry multiplier max_retries+1, CLI training folds/epochs. No global wall-clock or atomic budget bound. enumerate polls time every4096 visited leaves; claim caps only condition-passing cases, has no leaf-level time poll, and delegates evaluator checks.

### composition

Problem kind/source→Expect integer/options→gate; plan/curriculum normalizers and tolerances differ. Template substitution lossy then gate rechecks. CLI held policy outside run_c. Vmm cap precheck not reservation. Build output enters lex module; suite uses separate small-unit engine.

### domain

Bounded synthetic helpers/plans/records. Public module compile-only, classic CLI usage-only. Live teacher/Lean/models/corpora/held/DB/GPU and large benchmark excluded.

### limitations

Finite test floats, local compiler/filesystem; delegated arithmetic retains own limits. Lexical AST lacks semantic resolution/macros. No-panic perceptron comparisons require comparable non-NaN accumulated scores and weights; finite weights alone do not prevent score overflow/NaN.

### checks

- paired syntax for14 legacy sources
- twice debug/twice release native selections and normalized outcomes
- compiled assertion-inversion controls, exact restoration and rerun

### catalog

### behavior-complement

Verified B excludes failures/missing answer but not wrong NL model. Over-cap/Lean-ban preflights exclude only guarded effects.

### reverse-reconstruction

Records admit all antecedent plans/prompts producing those observations; template and summaries lose values/order/metadata so inverse is many-valued.

### expectation-join

Expect integer for int or number from TheoremQA, options verbatim. Numeric gate and grading differ in tolerance/normalization.

### fallback-state

Fallback copies answer/option/verified/correct/cost/tokens/secs/method, not B trace/history; keeps C config and by_slm=false.

### effect-order

Vmm cap→mkdir→teacher→spent→append→is_error; Lean bans→write→process→diagnostics. Failed append not rollback.

### budget-composition

Per-plan limits/reserve estimates do not bound parallel composition; concurrent prechecks can overspend.