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

The groupant beside world/src/ans.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/ans.rs`](https://github.com/ElamurAI/mova-free/blob/main/world/src/ans.rs)
- **source SHA-256:** `d8d94c891e347d2b…`
- **covers:** Rolling longest-common-subsequence row (bytes 64818–65164)
- **part of:** [world-ans-metric](https://md.groupants.elamur.ai/free/en/mova/world/src/ans.rs.groupant/metric.groupant/)
- **repository folder:** [`world/src/ans.rs.groupant/metric.groupant/lcs-row.groupant`](https://github.com/ElamurAI/mova-free/tree/main/world/src/ans.rs.groupant/metric.groupant/lcs-row.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 source model | [forward](#forward) |
| **ast** | partial | `../../syntax.json` |
| **composition** | partial source model | [parent-interaction](#parent-interaction) |
| **cost** | partial source model | [cost](#cost) |
| **descriptant** | partial source model | [epoch-memory](#epoch-memory) |
| **invariant** | partial source model | [invariant](#invariant) |
| **tests** | partial source model | [checks](#checks) |

## 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 |
|---|---|---|---|
| `world-ans-metric-lcs-row-behavior-complement` | behavior_complement | partial source model | [behavior-complement](#behavior-complement) |
| `world-ans-metric-lcs-row-reverse-reconstruction` | reverse_reconstruction | partial source model | [reverse-reconstruction](#reverse-reconstruction) |
| `world-ans-metric-lcs-row-parent-interaction` | composition_relation | partial source model | [parent-interaction](#parent-interaction) |
| `world-ans-metric-lcs-row-boundary` | constraint_relation | partial source model | [boundary](#boundary) |
| `world-ans-metric-lcs-row-information` | information_projection | partial source model | [information](#information) |
| `world-ans-metric-lcs-row-cost` | resource_relation | partial source model | [cost](#cost) |

## Model text


Wave34, 2026-10-31. Subject: world-ans-metric-lcs-row, current source SHA d8d94c891e347d2b640744b20c4662dc35064368e7d4d9253c4954b4297e1e09. Domain: one terminating supplied-input helper transition; valid indices, sufficient memory and finite strings/trees/worlds. Source-derived partial relations, not a verified universal theorem. All views below share this domain and exact manifest scope; specialized assumptions are stated locally. No executable percentage approximant is claimed.

### forward

For each a token keep saved previous-row diagonal; for each b token set cell to diagonal+1 on equality, else max(previous-row same column, current-row left). Return final cell.

### invariant

Returned length cannot exceed min(n,m); unequal singleton streams cannot return 1. Reordering tokens is not generally score-preserving.

### behavior-complement

Returned length cannot exceed min(n,m); unequal singleton streams cannot return 1. Reordering tokens is not generally score-preserving.

### reverse-reconstruction

A length k admits every sequence pair with longest common subsequence k; many matching witnesses and token spellings may realize it. k=0 contains disjoint alphabets and either empty sequence, without unique reconstruction.

### parent-interaction

rouge_l tokenizes first, bypasses empty streams, then consumes LCS for harmonic precision/recall; rouge_q takes best nonblank reference. DP length does not establish semantic answer quality.

### boundary

After column j, dp[j+1] is current-prefix optimum while prev is the previous-row diagonal for the next cell; overwriting prev too early destroys dependencies.

### information

Symmetry holds for returned length though space cost depends on the second input. Repeated equal tokens need distinct subsequence positions.

### cost

Exactly n*m inner iterations, m+1 usize cells, O(n*m) time and O(m) auxiliary memory excluding token input; no task-error surrogate.

### checks

Existing independent subset enumeration over 961 binary sequence pairs; finite test is not general correctness proof.

Exact selected native boundary: `cargo test --offline --locked -p world --lib ans::wave8_models::lcs_matches_subsequence_oracle -- --exact --test-threads=1`. Repeated in debug and release; see the current file-level wave34 evidence and external native-receipts.json.

### assurance

The behavior-complement is an inner exclusion hypothesis over admissible input/output pairs, derived from branch order; not the complement of an incomplete model of the entire file. Reverse reconstruction is the compatible antecedent relation, retaining every modeled ambiguity rather than a chosen inverse. Parent-interaction is a composition relation, boundary a constraint relation, information an information/state projection, and cost a resource relation. The named checks are finite falsifiers; unexecuted branches remain source-inspected gaps. No parser/model/teacher/corpus/frozen assessment was run.

### epoch-memory

New child in wave34; no prior child renamed or counted. Parent historical wave8/wave9 evidence remains historical. Current raw receipts are in the external wave34 reasoning run; source syntax is partial, macros opaque, and no semantic AST or general proof is supplied.