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

The groupant beside world/src/school.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/school.rs`](https://github.com/ElamurAI/mova-free/blob/main/world/src/school.rs)
- **source SHA-256:** `06aaec6f562c2acc…`
- **covers:** Op::apply uses checked Add/Mul, checked Sub only when a>=b, and Div only for exact representable quotients. Problem::answer maps None to legacy zero. Fixed xorshift and template filtering assemble the elementary curriculum; revision sorts last. (bytes 1552–14464)
- **part of:** [world-school](https://md.groupants.elamur.ai/free/en/mova/world/src/school.rs.groupant/)
- **repository folder:** [`world/src/school.rs.groupant/arithmetic-curriculum.groupant`](https://github.com/ElamurAI/mova-free/tree/main/world/src/school.rs.groupant/arithmetic-curriculum.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-school-arithmetic-curriculum-behavior-complement` | behavior_complement | partial source model | [behavior-complement](#behavior-complement) |
| `world-school-arithmetic-curriculum-reverse-reconstruction` | reverse_reconstruction | partial source model | [reverse-reconstruction](#reverse-reconstruction) |
| `world-school-arithmetic-curriculum-coupling` | constraint_relation | partial source model | [coupling](#coupling) |
| `world-school-arithmetic-curriculum-observation-fiber` | information_loss | partial source model | [observation-fiber](#observation-fiber) |

## Model text


### forward

Op::apply uses checked Add/Mul, checked Sub only when a>=b, and Div only for exact representable quotients. Problem::answer maps None to legacy zero. Fixed xorshift and template filtering assemble the elementary curriculum; revision sorts last.

### invariant

Sub never returns negative; Div rejects zero, nonzero remainder and MIN/-1. Signed Add/Mul/Div results are allowed. PRACTICE and TEST have distinct complete strings, not disjoint vocabulary. Rng range requires a valid small inclusive range and pick a nonempty slice.

### cost

Arithmetic O(1); template generation linear output bytes; lesson sorting O(L log L). Checked scalar arithmetic keeps the original asymptotic cost. No performance optimization claimed.

### composition

Problem::answer and Student::answer share apply. Public Problem admits arbitrary i64, unlike bounded generators. The native oracle uses i128 for 25x25x4 rows; five extreme cases reject overflow. Template separation and revision order are constant-only checks.

### epoch-memory

2026-10-30 initial school source-bound epoch. Prospective model: keep O(1) arithmetic/partition cost, widen aggregation scalars, and expose actual codecs without filesystem effects. Old native witnesses found unchecked operation, score, marginal vote, partition and duplicate-vote arithmetic; legacy serialization synthesized zero accumulators. Review found that dropping explicit zero accumulators also changed the prediction table. Both activation directions now have named tests. No speedup, approximate-error profile or general semantic proof is claimed. Unchecked update/world arithmetic retains representability premises.

### checks

cargo test -p world --lib school::wave12_models -- --test-threads=1. Root evidence.md binds exact source/evidence hashes, repeated debug/release outcomes and a compiled production mutation. Named fixture domains appear in composition. Syntax is a source-bound partial projection; macros remain opaque. No semantic AST or live school execution.

### behavior-complement

Subject/revision: manifest hash and byte scope. Universe: supplied finite inputs, fixed dependencies, successful allocation and the explicit arithmetic premises of this scope. Inner absent-behavior relation: Some(z) is absent for overflow, a<b subtraction, zero divisor, inexact division and MIN/-1. The model excludes results different from the exact representable equation. Invalid Rng inputs remain outside scope. These are source-derived constraints with finite named witnesses where indicated; external behavior remains unknown.

### reverse-reconstruction

Subject/revision: manifest hash. Operator: compatible preimage/converse, holding dependencies and admissibility fixed. For fixed op,z retain all i64 pairs satisfying the operation equation and its guards. Add(z=0) includes (0,0),(1,-1); Mul(z=0) has both zero-axis fibers. Problem::answer(0) also admits invalid operations, so its scalar result cannot recover success. Partial relational description, not a complete inverse search or a unique causal history.

### coupling

Subject/revision: manifest hash. Constraint relation on stage identities and ordered intermediate states: Problem::answer and Student::answer share apply. Public Problem admits arbitrary i64, unlike bounded generators. The native oracle uses i128 for 25x25x4 rows; five extreme cases reject overflow. Template separation and revision order are constant-only checks. Supplied native joins and source inspection are distinct evidence.

### observation-fiber

Subject/revision: manifest hash. Domain: scoped inputs with the declared observation. The information-loss relation equates inputs whose observation agrees: Invalid arithmetic collides with genuine zero through Problem::answer's legacy fallback. Retain Option from apply when successful zero must remain distinguishable. Finite tests do not establish unrestricted completeness.