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

The groupant beside world/src/stepgame.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/stepgame.rs`](https://github.com/ElamurAI/mova-free/blob/main/world/src/stepgame.rs)
- **source SHA-256:** `56231f07cd9c54f1…`
- **covers:** Validate two query agents; create v and -v for each two-agent sentence; seed q1 zero and assign vacant neighbors through BFS. Return sign label and deduplicated suspect-id count. BFS recurrence p[q1]=0 and p[y]=p[x]+v when y unassigned; answer label is sign(p[q0]); if q0 absent then None. Reader fallback uses pred=min argmax_k Σ_f w[f,k]. (bytes 14286–15569)
- **part of:** [world-stepgame](https://md.groupants.elamur.ai/free/en/mova/world/src/stepgame.rs.groupant/)
- **repository folder:** [`world/src/stepgame.rs.groupant/graph.groupant`](https://github.com/ElamurAI/mova-free/tree/main/world/src/stepgame.rs.groupant/graph.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) |
| **cost** | partial | [Cost](#cost) |
| **descriptant** | present | [descriptant](#descriptant) |
| **invariant** | partial | `model.md` |
| **tests** | bounded checks partial scope | [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) |
| `origin` | origin | partial source derived model | [origin](#origin) |
| `empty_story` | empty_story | partial source derived model | [empty_story](#empty-story) |
| `read_boundary` | read_boundary | partial source derived model | [read_boundary](#read-boundary) |
| `sign_projection` | sign_projection | partial source derived model | [sign_projection](#sign-projection) |

## Model text


### descriptant

#### world-stepgame-graph

Validate two query agents; create v and -v for each two-agent sentence; seed q1 zero and assign vacant neighbors through BFS. Return sign label and deduplicated suspect-id count. BFS recurrence p[q1]=0 and p[y]=p[x]+v when y unassigned; answer label is sign(p[q0]); if q0 absent then None. Reader fallback uses pred=min argmax_k Σ_f w[f,k].

##### Modeling epoch — 2026-10-31

Read full assigned source before editing; prospective predictions retained in external wave29 receipts. This child binds only its stated half-open UTF-8 byte range; other APIs remain parent scope. Evidence is limited to named bounded fixtures; registration is partial modeling. Production behavior unchanged; only inline synthetic tests added to four assigned sources.

### approximant

#### Forward relation

Validate two query agents; create v and -v for each two-agent sentence; seed q1 zero and assign vacant neighbors through BFS. Return sign label and deduplicated suspect-id count. BFS recurrence p[q1]=0 and p[y]=p[x]+v when y unassigned; answer label is sign(p[q0]); if q0 absent then None. Reader fallback uses pred=min argmax_k Σ_f w[f,k].

##### Domain and resource limits

Finite valid structures and allocation-success executions under the branch conditions in models.md; integer overflow is outside measured fixtures. Exact categorical relations have no supplied percent surrogate. Macro expansion, arbitrary model quality and external effects are not inferred from syntax.

### invariant

## Invariant

Adjacency insertion order breaks path ties; suspect count is distinct ids despite message saying sentences.

### Cost

Story reader cost plus O((V+E)logV), clones and suspect search; i32 addition unchecked.

### composition

#### Composition

This scope contributes graph to its parent. Its forward, complement and preimage are restricted to the bound byte interval. The parent syntax projection is referenced once through ../syntax.json; no independent semantic AST is claimed.

### models

### behavior_complement

Exclude result for unreachable target or one deduplicated query agent. Inconsistent cycles are not reconciled.

### reverse_reconstruction

Left fiber comprises Reader/story states with negative x,zero y first-path target displacement; exact diagnostic offset leaves graph underdetermined. Pre(left)={(R,I):p[q0]=(x,0),x<0}; Pre(label,offset=d) additionally constrains p[q0]=d.

### origin

q[1] zero; edge a1→a0 adds read(a0,a1).

### empty_story

No valid edges leaves distinct query target unreachable.

### read_boundary

Fixture marks phrasing seen to force zero-weight perceptron regardless of lexical environment.

### sign_projection

-2,0 and -1,0 both left; explanation retains magnitude.

### tests

#### Bounded checks

Named checks associated with this source (not every fragment branch):

- stepgame::wave29_tests::lexical_ground_and_tie_boundaries
- stepgame::wave29_tests::graph_first_path_and_text_reset
- tests03::stepgame_lexical_reader_reads_new_phrasings
- tests03::stepgame_phrasing_and_corrected_format

17 unique named tests in total passed twice debug and twice release; sorted named outcomes equal across all four runs. Four compiled controls cover bAbI identity, StepGame tie ordering, parser-command state removal and bench-command CPU selection; each exits101 at a runtime assertion, exact source restored then positive exit0. Other sources have finite adversarial fixtures but no separately compiled mutant.

CLI integration coverage is command construction and temporary cleanup only; legacy school/model/cadence paths are not executed. No speed benchmark, GPU, live teacher, datasets or held-out replay.

Limits:

- Partial syntax projection only; no macro expansion or proof
- No useful percentage surrogate for exact categorical/state/effect semantics; executable approximant unsupported
- No dataset training, eval/contrast or GPU
- No overflow/allocation fault injection

External receipt root: $MOVA_DATA/runs/octopus-wave29-worldeval-2026-10-31.