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

This page as HTML: <https://groupants.elamur.ai/free/en/mova/world/src/babi.rs.groupant/graph.groupant/>

# world-babi-graph

The groupant beside world/src/babi.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/babi.rs`](https://github.com/ElamurAI/mova-free/blob/main/world/src/babi.rs)
- **source SHA-256:** `54596da093fa9515…`
- **covers:** holds canonicalizes relation then uses dot(offset,vec)>0 for vectors or forward reach before inverse reach for transitive relations. offset BFS subtracts signed adjacency vectors. path BFS retains first predecessor and reverses collected steps. Equations: pos[b]=(0,0); on first edge y→x carrying v set pos[x]=pos[y]−v. holds(a,r,b)=Some(pos[a]·vec(r)>0) when reachable. Transitive truth is reach_r(a,b), else false if reach_inverse(r)(a,b), else None. (bytes 25318–29716)
- **part of:** [world-babi](https://md.groupants.elamur.ai/free/en/mova/world/src/babi.rs.groupant/)
- **repository folder:** [`world/src/babi.rs.groupant/graph.groupant`](https://github.com/ElamurAI/mova-free/tree/main/world/src/babi.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) |
| `axis_predicate` | axis_predicate | partial source derived model | [axis_predicate](#axis-predicate) |
| `path_order` | path_order | partial source derived model | [path_order](#path-order) |
| `inverse_edges` | inverse_edges | partial source derived model | [inverse_edges](#inverse-edges) |
| `metadata_gate` | metadata_gate | partial source derived model | [metadata_gate](#metadata-gate) |

## Model text


### descriptant

#### world-babi-graph

holds canonicalizes relation then uses dot(offset,vec)>0 for vectors or forward reach before inverse reach for transitive relations. offset BFS subtracts signed adjacency vectors. path BFS retains first predecessor and reverses collected steps. Equations: pos[b]=(0,0); on first edge y→x carrying v set pos[x]=pos[y]−v. holds(a,r,b)=Some(pos[a]·vec(r)>0) when reachable. Transitive truth is reach_r(a,b), else false if reach_inverse(r)(a,b), else None.

##### 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

holds canonicalizes relation then uses dot(offset,vec)>0 for vectors or forward reach before inverse reach for transitive relations. offset BFS subtracts signed adjacency vectors. path BFS retains first predecessor and reverses collected steps. Equations: pos[b]=(0,0); on first edge y→x carrying v set pos[x]=pos[y]−v. holds(a,r,b)=Some(pos[a]·vec(r)>0) when reachable. Transitive truth is reach_r(a,b), else false if reach_inverse(r)(a,b), else None.

##### 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

offset(b,b)=(0,0), path(b,b)=[] even absent nodes; vertices assigned once.

### Cost

reach O(VE); ordered-map BFS O((V+E)log V), string/adjacency cloning extra; i32 overflow outside fixture domain.

### 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 a displacement across disconnected nodes or nonempty self path. Contradictory graphs are not rejected; first path or forward reach wins.

### reverse_reconstruction

True vector predicate admits all reachable d with d·vec(r)>0. Path [e,n] admits all graphs with that first shortest-path labeling; other edges and lengths remain underdetermined. Pre(true;r,a,b)={G | BFS_G(b)[a]=d ∧ d·vec(r)>0}.

### axis_predicate

north_of requires positive y regardless of x; zero dot gives false when reachable.

### path_order

Relation insertion order decides competing equal-length paths.

### inverse_edges

A north_of B gives B→A north and reverse south.

### metadata_gate

Missing vec omits offset edges; missing step or inverse step omits path edges.

### tests

#### Bounded checks

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

- babi::wave29_tests::identity_and_inventory_without_parser
- babi::wave29_tests::graph_and_sentence_boundaries_without_parser

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 live parser, corpus, gap journal, training or held-out evaluation
- Unicode recasing byte slices, unbounded recursion/overflow not covered

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