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

The groupant beside world/src/lessons.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:** [`world/src/lessons.rs`](https://github.com/ElamurAI/mova-free/blob/main/world/src/lessons.rs)
- **source SHA-256:** `c095c4c5f7556a32…`
- **covers:** At most 2000 attempts: bind variables in order, derive lets in order, require all needs nonzero, evaluate nonnegative answer, fill selected template k modulo template count. Empty templates fail before RNG mutation. Exhausted unique names and invalid/reversed ranges fail. Inclusive numeric sampling uses i128 width and u128 residue, including full i64 domain. Wrapping seed addition defines large lesson numbers. (bytes 11561–14772)
- **part of:** [world-lessons](https://md.groupants.elamur.ai/free/en/mova/world/src/lessons.rs.groupant/)
- **repository folder:** [`world/src/lessons.rs.groupant/draw.groupant`](https://github.com/ElamurAI/mova-free/tree/main/world/src/lessons.rs.groupant/draw.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 source model | [forward](#forward) |
| **ast** | partial | `../syntax.json` |
| **composition** | partial source model | [composition](#composition) |
| **cost** | partial source model | [cost](#cost) |
| **descriptant** | partial source model | [epoch-memory](#epoch-memory) |
| **invariant** | partial source model | [invariant](#invariant) |
| **tests** | partial source model | [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 |
|---|---|---|---|
| `world-lessons-draw-behavior-complement` | behavior_complement | partial source model | [behavior-complement](#behavior-complement) |
| `world-lessons-draw-reverse-reconstruction` | reverse_reconstruction | partial source model | [reverse-reconstruction](#reverse-reconstruction) |
| `world-lessons-draw-coupling` | constraint_relation | partial source model | [coupling](#coupling) |

## Model text


### forward

At most 2000 attempts: bind variables in order, derive lets in order, require all needs nonzero, evaluate nonnegative answer, fill selected template k modulo template count. Empty templates fail before RNG mutation. Exhausted unique names and invalid/reversed ranges fail. Inclusive numeric sampling uses i128 width and u128 residue, including full i64 domain. Wrapping seed addition defines large lesson numbers.

### behavior-complement

U is lesson/RNG/template/index inputs and output/final-RNG pairs with bounded expressions and helper domains. Absent success includes negative answer, unsatisfied conditions, exhausted names, reversed intervals and empty templates. Exhaustion returns None rather than guaranteeing a sample.

### reverse-reconstruction

B(d,s1) includes all initial seeds and rejected-attempt histories that produce d and final RNG s1. Modulo reductions and dropped variables lose information. Output alone cannot recover attempt count or template identity.

### coupling

Same seed and supplied lesson reproduce text/answer. Exercises/test/exam choose distinct containers and seed constants, but neither seed separation nor containers prove content disjointness. RNG(0) is an absorbing state; no uniformity promise. Failed attempts consume RNG state except early structural rejection.

### invariant

Successful observations obey the declared forward relation with the same supplied state and order. Failure is explicit; no hidden label or retained-state guarantee is introduced.

### cost

Bound 2000 times variable binding, expression and render costs. Name filtering bounded by 16-name table. Batch cost multiplies by requested count; accepted count can be smaller. No live learning or persistence modeled.

### composition

Evaluation and substitution share numeric bindings; field labels choose template containers. Child relations must agree on intermediate state, not merely final counts. Partial syntax binds the source; macro contents are opaque.

### epoch-memory

Initial review predicted arithmetic overflow and finite-pool boundary failures. Old native code failed six named witnesses: overflow, empty templates, name exhaustion, full-width range, reversed range and seed overflow. Narrow repairs retain public signatures; finite observations do not establish arbitrary-input totality. See file evidence.md for hashes and repeated results.

### checks

Eight wave12_models tests plus two existing lesson tests. Independent 19 by 19 by 7 arithmetic cases, precedence/eager failure literals, partition/substitution fixtures and exactly 2000 rejected RNG draws. Runtime guard mutations must fail named assertions. Evidence is finite; no whole-world or live course claim.