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

The groupant beside tools/treeagree/src/tree.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:** [`tools/treeagree/src/tree.rs`](https://github.com/ElamurAI/mova-free/blob/main/tools/treeagree/src/tree.rs)
- **source SHA-256:** `6e034fd13c47961f…`
- **covers:** arc-crossing (bytes 6782–7234)
- **part of:** [treeagree-tree](https://md.groupants.elamur.ai/free/en/mova/tools/treeagree/src/tree.rs.groupant/)
- **repository folder:** [`tools/treeagree/src/tree.rs.groupant/arc-crossing.groupant`](https://github.com/ElamurAI/mova-free/tree/main/tools/treeagree/src/tree.rs.groupant/arc-crossing.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 | `model.md` |
| **ast** | partial | `../syntax.json` |
| **composition** | partial | [Composition](#composition) |
| **cost** | partial | [invariant-and-cost](#invariant-and-cost) |
| **descriptant** | present | [descriptant](#descriptant) |
| **invariant** | partial | [invariant-and-cost](#invariant-and-cost) |
| **tests** | bounded checks | [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) |
| `root_erasure` | root_erasure | partial source derived model | [root_erasure](#root-erasure) |
| `endpoint_symmetry` | endpoint_symmetry | partial source derived model | [endpoint_symmetry](#endpoint-symmetry) |
| `strict_boundary` | strict_boundary | partial source derived model | [strict_boundary](#strict-boundary) |
| `index_domain` | index_domain | partial source derived model | [index_domain](#index-domain) |

## Model text


### descriptant

#### Descriptant

For one-based i, root arc returns false; otherwise scan other nonroot arcs for strict alternating endpoints a<c<b<d or c<a<d<b.

##### Epoch 2026-10-31

Prospective source reading identified conditional input alignment, information loss and failure order before tests. Existing production code is retained; added tests use actual helpers. Finite results update this source-bound model, not all parser/corpus semantics.

No executable percentage surrogate has a justified observation metric for these categorical/effectful APIs. Future profiles require metric, domain and real-reference evidence at caps 1/2/5/10%; no higher cap. Syntax is partial lexical Rust projection without macro expansion or semantic resolution.

### approximant

## Forward approximant

For one-based i, root arc returns false; otherwise scan other nonroot arcs for strict alternating endpoints a<c<b<d or c<a<d<b.

### Composition

This fragment is the exact byte-scoped helper identified in the manifest; its relation is restricted to the operations above.

The containing source wires this scoped relation to its callers. Treeagree proposal→gate→commit and treebanks parse→match→collect→render are actual joins; parsecmp is an independent diagnostic path. The external group model distinguishes these tags.

### catalog

## Typed models for treeagree-tree-arc-crossing

Subject: source SHA-256 `6e034fd13c47961fb03e46caddbd17d7ec53d236af64ea9cb2a46bdc3834f8fd`; manifest supplies exact source/byte scope. Domain: admitted states in forward model, nonoverflow arithmetic and successful allocations. Observation: one terminating invocation, except explicitly described file trace. Source-derived partial relations; named finite tests constrain selected cases only. Each entry holds arguments and environment fixed except its stated intervention.

### behavior_complement

Identical arcs, nested intervals and shared endpoints cannot alone witness crossing.

Operator: inner exclusion on admitted domain. Evidence: source branch derivation plus tests.md; unexercised branches remain hypotheses. Oracle: evaluate the scoped actual helper on admissible fixtures and compare this observation. No universal proof.

### reverse_reconstruction

true identifies existence of some interleaving arc, not its identity; false admits all noninterleaving families and arbitrary root arcs.

Operator: compatible antecedent relation, retaining ambiguity. Evidence: source branch derivation plus tests.md; unexercised branches remain hypotheses. Oracle: evaluate the scoped actual helper on admissible fixtures and compare this observation. No universal proof.

### root_erasure

A head zero arc is excluded both as queried arc and potential witness.

Operator: specialized observation relation under the stated fixed inputs. Evidence: source branch derivation plus tests.md; unexercised branches remain hypotheses. Oracle: evaluate the scoped actual helper on admissible fixtures and compare this observation. No universal proof.

### endpoint_symmetry

Swapping orientation of the same two nonroot endpoints preserves crossing predicate.

Operator: specialized observation relation under the stated fixed inputs. Evidence: source branch derivation plus tests.md; unexercised branches remain hypotheses. Oracle: evaluate the scoped actual helper on admissible fixtures and compare this observation. No universal proof.

### strict_boundary

Equality at any interleaving boundary makes that conjunction false; touching differs from crossing.

Operator: specialized observation relation under the stated fixed inputs. Evidence: source branch derivation plus tests.md; unexercised branches remain hypotheses. Oracle: evaluate the scoped actual helper on admissible fixtures and compare this observation. No universal proof.

### index_domain

i=0 or i>len panics rather than returning a graph-validation error; callers must provide valid one-based position.

Operator: specialized observation relation under the stated fixed inputs. Evidence: source branch derivation plus tests.md; unexercised branches remain hypotheses. Oracle: evaluate the scoped actual helper on admissible fixtures and compare this observation. No universal proof.

### tests

#### Scoped evidence

Parent native slice and exact names are in `../tests.md`.

Only named finite assertions cover selected inputs; other branches and invalid-domain behavior remain source-derived.

This fragment has no independent full-coverage claim. Its byte range and source hash bind the source-derived relation; parent test success is evidence only where that helper is actually reached.

### invariant-and-cost

#### Invariant and cost

O(n) head scans and O(1) auxiliary space; i must index heads.

Identical arcs, nested intervals and shared endpoints cannot alone witness crossing.

The complement and specialized catalog constrain preserved coordinates and effect boundaries. Empty/malformed domains are only guaranteed where explicitly admitted. No whole-program cost bound follows from a helper bound.