---
title: "rt-mixed-diff-lcs — Mova code model"
description: "Mova code model of tools/roundtrip/src/diff.rs: components with their labels, obernants and the model text."
url: "https://groupants.elamur.ai/free/en/mova/tools/roundtrip/src/diff.rs.groupant/lcs.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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# rt-mixed-diff-lcs

The groupant beside tools/roundtrip/src/diff.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/roundtrip/src/diff.rs`](https://github.com/ElamurAI/mova-free/blob/main/tools/roundtrip/src/diff.rs)
- **source SHA-256:** `dc8f0bd667aee979…`
- **covers:** Suffix DP uses equal-form diagonal+1 else max; traversal advances original on ties. (bytes 866–1521)
- **part of:** [rt-mixed-diff](https://md.groupants.elamur.ai/free/en/mova/tools/roundtrip/src/diff.rs.groupant/)
- **repository folder:** [`tools/roundtrip/src/diff.rs.groupant/lcs.groupant`](https://github.com/ElamurAI/mova-free/tree/main/tools/roundtrip/src/diff.rs.groupant/lcs.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** | partial | [approximant](#approximant) |
| **ast** | partial | `../syntax.json` |
| **cost** | symbolic source derived | [invariant](#invariant) |
| **descriptant** | present | [descriptant](#descriptant) |
| **invariant** | partial | [invariant](#invariant) |
| **tests** | executed 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) |
| `score_bounds` | score_bounds | partial source derived model | [score_bounds](#score-bounds) |
| `tie_direction` | tie_direction | partial source derived model | [tie_direction](#tie-direction) |
| `form_only` | form_only | partial source derived model | [form_only](#form-only) |
| `quadratic_storage` | quadratic_storage | partial source derived model | [quadratic_storage](#quadratic-storage) |

## Model text


### descriptant

#### Descriptant

##### Prospective epoch

2026-10-31 source review predicted: Suffix DP uses equal-form diagonal+1 else max; traversal advances original on ties. Resource model: O(n*m) DP time and memory, plus form comparison bytes; reconstruction O(n+m). External prospective.md predates test additions and preserves APIs, effect order, hazards and interaction hypotheses.

##### Observed epoch

Bounded real helper checks in tests.md constrain these models; syntax is a partial lexical projection with no macro expansion, name resolution or proof. Production expressions unchanged; six inline test modules added. Compiled mutants are temporary and exactly restored. Existing malformed-input and nonfinite domains remain explicit, not silently repaired. Parent composes this scope with siblings without adding overlapping costs twice.

Narrow Form LCS alignment scope; finite checks do not cover all inputs. Parent effects and other functions are outside this fragment.

### approximant

#### Forward relation

Suffix DP uses equal-form diagonal+1 else max; traversal advances original on ties.

Domain: Scope: Form LCS alignment. Valid token fields, lengths fit allocation and u32 LCS/counters. Exact strings can bypass inconsistent Tk fields; token coordinates are indices, cut truncates90 Unicode scalars.

### invariant

#### Invariant and cost

##### Invariant

Scope: Form LCS alignment. Valid token fields, lengths fit allocation and u32 LCS/counters. Exact strings can bypass inconsistent Tk fields; token coordinates are indices, cut truncates90 Unicode scalars.

##### Cost

O(n*m) DP time and memory, plus form comparison bytes; reconstruction O(n+m).

##### Limits

Narrow Form LCS alignment scope; finite checks do not cover all inputs. Parent effects and other functions are outside this fragment. No percentage surrogate is implemented: categorical parsing/effect observations lack an admitted numerical error metric. Any future profile must define its metric/domain and use only1/2/5/10 percent caps.

### models

## Typed source-bound relations

Subject: exact source SHA-256 in manifest. Domain and resource premises are in invariant.md. Each model is partial, source-derived, over a single helper invocation or the described finite trace. Complements are proposed inner exclusions under those premises; reverse relations retain all compatible antecedents, with no unique inverse claim. The oracle is the named checks in tests.md; unexecuted cases remain hypotheses. No numerical approximation certificate.

### behavior_complement

Within this scoped helper relation, outputs violating the stated forward equation or its preserved fields are excluded under the domain premises; this is a partial source-derived inner exclusion, not a claim about untested panics. u32 score<=min(n,m) within admitted size.

### reverse_reconstruction

Witness pairs do not recover mismatched tokens; repeated equal forms have other optimal alignments.

### score_bounds

u32 score<=min(n,m) within admitted size

### tie_direction

unequal forms with equal suffix scores advance i

### form_only

lemma/tag/rel/space ignored by LCS

### quadratic_storage

(n+1)*(m+1) u32 cells allocated before traversal

### tests

#### Checks and evidence

Named source/helper checks: diff::tests::classes_of_changes.

Wave32 on2026-10-31:10 distinct exact tests passed twice debug and twice release, with equal sorted named outcomes. This node claims only its listed subset; empty subset means source review only. Five actual source-behavior mutants compiled, failed assertions, restored exact bytes/hash, and passed focused green reruns. No assertion-only mutants; existing swapped-input controls are separate. Receipt bundle: $MOVA_DATA/runs/octopus-wave32-rt_mixed-2026-10-31 (native-commands.json, source-test-map.json, mutation-results.json, *.status/*.log). No live corpus, teacher, frozen assessment, download or production data used.

Narrow Form LCS alignment scope; finite checks do not cover all inputs. Parent effects and other functions are outside this fragment.