---
title: "algorithm-functional-graph-decomposition — Mova code model"
description: "Mova code model of algorithms/src/functional_graph_decomposition/mod.rs: components with their labels, obernants and the model text."
url: "https://groupants.elamur.ai/free/en/mova/algorithms/src/functional_graph_decomposition/mod.rs.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/algorithms/src/functional_graph_decomposition/mod.rs.groupant/>

# algorithm-functional-graph-decomposition

The groupant beside algorithms/src/functional_graph_decomposition/mod.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
- **status:** partial source derived instance
- **source:** [`algorithms/src/functional_graph_decomposition/mod.rs`](https://github.com/ElamurAI/mova-free/blob/main/algorithms/src/functional_graph_decomposition/mod.rs)
- **source SHA-256:** `ff41869319484740…`
- **repository folder:** [`algorithms/src/functional_graph_decomposition/mod.rs.groupant`](https://github.com/ElamurAI/mova-free/tree/main/algorithms/src/functional_graph_decomposition/mod.rs.groupant)
- **repository commit:** `855da7bd4a7b`

> **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** | source derived | [Forward](#forward) |
| **ast** | partial | `syntax.json` |
| **cost** | symbolic unmeasured | [Cost](#cost) |
| **descriptant** | present | [descriptant](#descriptant) |
| **invariant** | source derived | [Invariant](#invariant) |
| **tests** | bounded executed | [evidence](#evidence) |

## 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 |
|---|---|---|---|
| `nonbehavior` | behavior_complement | partial source derived | [nonbehavior](#nonbehavior) |
| `preimages` | reverse_reconstruction | partial source derived | [preimages](#preimages) |
| `transition` | specialized_relation | partial source derived | [transition](#transition) |
| `order` | specialized_relation | partial source derived | [order](#order) |
| `coordinate` | specialized_relation | partial source derived | [coordinate](#coordinate) |
| `fiber` | specialized_relation | partial source derived | [fiber](#fiber) |
| `errors` | error_partition | partial source derived | [errors](#errors) |

## Model text


Migration: consolidated into model.md, 2026-11-04, operator decision; fresh hash-bound references to the former files were rebound to the sections below.

### descriptant

#### algorithm-functional-graph-decomposition

Original std-only implementation or original independent fixtures. See source citations. Prospective model was saved before implementation in $MOVA_DATA/runs/octopus-wave26-combinatorial-2026-10-30/prospective.md.

Preserve original coordinates, deterministic ties and distinct validation/resource/infeasibility outcomes. Repeated observations constrain this epoch only.

### model

## algorithm-functional-graph-decomposition

### Domain

<=1000000 valid zero-based successors; cycles, per-vertex cycle ID, original entry coordinate, distance.

### Forward

Peel indegree-zero tails; enumerate residual cycles from least unseen original coordinate in successor order; reverse peeling propagates entry, ID and distance.

### Invariant

Every vertex belongs to exactly one eventual cycle; entry is first cycle vertex encountered and distance is the exact number of successor applications to entry.

### Cost

O(V) time and memory.

### nonbehavior

Type: behavior_complement.

Exclude wrong coordinate conventions, noncanonical cycle rotations/order, positive cycle distances, or entries not reached at the reported distance.

### preimages

Type: reverse_reconstruction.

Cycles reconstruct successor edges on cycle vertices exactly. Tail v with distance d>0 may point to any vertex with same entry and distance d-1, so tail predecessors are generally ambiguous. These choices reconstruct exactly the decomposition under canonical IDs.

### transition

Type: specialized_relation.

For noncycle v, distance[v]=distance[successor[v]]+1 and entry and ID are inherited.

### order

Type: specialized_relation.

Cycle vertices have entry[v]=v and distance zero; listed cycle orientation follows successor.

### coordinate

Type: specialized_relation.

Relabeling preserves distances and cycle membership but recanonicalizes cycle IDs/rotations.

### fiber

Type: specialized_relation.

Deleting a leaf tail preserves remaining entry coordinates and distances while coordinate renumbering must be explicit.

### errors

Type: error_partition.

Public size caps precede input-order validation, then arithmetic/search. Exact cover budget exhaustion is not infeasibility; closure capacity overflow is not infeasibility. Bounded index arithmetic cannot overflow. Checked i128 arborescence arithmetic remains defensive. Allocation failure is process-level, not returned; no callbacks or external writes. Empty cases and deterministic ties follow API docs.

### Limits

Partial syntax, no macro expansion/type resolution or full formal proof. No justified generic numerical surrogate for categorical witnesses/errors; supported 1/2/5/10% profiles remain absent, not fabricated. No timing claims. Allocation failure untested.

### evidence

#### Evidence

2026-10-30: All successor functions up to six vertices (50070 cases including empty); independent per-start walk until repetition validates entry, distance and cycle edges.

Two debug and two release runs, compiled mutation detected by coordinates_and_errors, restored positive rerun, strict all-target Clippy and twice-identical partial syntax. Logs: $MOVA_DATA/runs/octopus-wave26-combinatorial-2026-10-30. No timing measurement. Allocation failures and defensive i128 overflow unexercised.