---
title: "correspondence-lcs-bridges — Mova code model"
description: "Mova code model of tools/correspondence/tests/lcs_bridges.rs: components with their labels, obernants and the model text."
url: "https://groupants.elamur.ai/free/en/mova/tools/correspondence/tests/lcs_bridges.rs.groupant/"
---
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# correspondence-lcs-bridges

The groupant beside tools/correspondence/tests/lcs_bridges.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 bound model
- **source:** [`tools/correspondence/tests/lcs_bridges.rs`](https://github.com/ElamurAI/mova-free/blob/main/tools/correspondence/tests/lcs_bridges.rs)
- **source SHA-256:** `a321f2ae229f0d4d…`
- **repository folder:** [`tools/correspondence/tests/lcs_bridges.rs.groupant`](https://github.com/ElamurAI/mova-free/tree/main/tools/correspondence/tests/lcs_bridges.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** | partial source derived | [Forward](#forward) |
| **ast** | partial | `syntax.json` |
| **composition** | partial | [Composition](#composition) |
| **cost** | symbolic unmeasured | [Cost](#cost) |
| **descriptant** | present | [descriptant](#descriptant) |
| **invariant** | partial | [Invariant](#invariant) |
| **tests** | bounded executed | [Epoch memory and checks](#epoch-memory-and-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 |
|---|---|---|---|
| `behavior_complement` | behavior_complement | partial source derived | [behavior_complement](#behavior-complement) |
| `reverse_reconstruction` | reverse_reconstruction | partial source derived | [reverse_reconstruction](#reverse-reconstruction) |
| `histogram_exclusion` | specialized_relation | partial source derived | [histogram_exclusion](#histogram-exclusion) |
| `comparison_schedule` | specialized_relation | partial source derived | [comparison_schedule](#comparison-schedule) |
| `unit_boundary` | specialized_relation | partial source derived | [unit_boundary](#unit-boundary) |

## Model text


### descriptant

#### LCS correspondence bridges

Six focused tests tie the production `en::text::lcs` to the two algorithm LCS implementations, an exhaustive oracle, one shared typed contract in the catalogue and the histogram upper bound as a partial exclusion. The comparison-schedule probe protects an API obligation that byte equality alone cannot see. See model.md for forward behavior, typed views, controls and epoch memory.

### model

## LCS correspondence probe model

### Forward
Compiled production sources plus the embedded catalogue. Exhaustive byte pairs: alphabet 2 through length 5 (63² pairs) call `en::text::lcs`, `longest_common_subsequence::length`, `bit_parallel_lcs::length` and a brute-force subsequence oracle; alphabet 3 through length 4 (121² pairs) call `en::text::lcs`, `longest_common_subsequence::length` and the oracle only, without bit-parallel. All lengths must agree. Seven fixtures bind rows `lcs.ordinary`, `lcs.algorithm`, `lcs.bitparallel`; `mova_correspondence::compare` must report `finite_coincidence` between the ordinary row and each algorithm row.

### Invariant
All three rows carry one identical contract: listed byte fixtures, symmetric byte equality, length-only observation, shorter side at most 64, successful returns. Implementation schedules and costs live in the source groupants. Finite success never promotes to universal equivalence.

### Cost
63² pairs with three library calls plus the oracle, 121² pairs with two library calls plus the oracle (at most 2⁵ masks each); fixtures are constant; catalogue JSON is reparsed per helper call. No timing is measured here.

### behavior_complement
Within the fixture universe, failure is a length disagreement, a wrong label, an absent output label, a wrong indexed pair, a schedule trace that is not a-major with the left receiver, or a bit-parallel `Ok` for a 65-byte short side. Untested inputs are unsupported, not excluded.

### reverse_reconstruction
Success admits any source satisfying these traces and tables; `(L,|a|,|b|)` has many antecedents ([1,2]/[2,1] and [1,3]/[1,4] both give 1). Hashes narrow identity only.

### histogram_exclusion
`Σ_t min(count_a(t),count_b(t))` is an independently computed upper bound: on the 7×4 rectangle it excludes 10 pairs, all disjoint from the three forward tables. It is a partial exclusion: `[1,2]/[2,1]→2` survives the bound while the actual value is 1, so the bound is not generally equal to the LCS and must not be substituted for the value; the catalogue holds no complement row for it.

### comparison_schedule
An asymmetric logging `PartialEq` records `(x.id, y.id, receiver side)`. `en::text::lcs` must produce exactly |a|·|b| probes in a-major order with the left element as receiver; the swapped call yields only right-side receivers and, under the asymmetric equality, zero. This obligation is specific to the ordinary API and is outside the shared length-only contract.

### unit_boundary
`"éa"` versus `"aé"`: one as characters, two as raw UTF-8 bytes. Bit-parallel accepts a 64-byte short side and rejects 65 with `ShortSideTooLong`; the two other APIs agree at 65.

### Composition
Production calls → length labels → indexed relation assertions → library compare on identical contracts. Correct lengths alone cannot certify label wiring; the negative controls swap distinct actual outputs (indices 0 and 2), truncate the domain, and append one assumption to show `incompatible_contract`.

### Epoch memory and checks
2026-10-31 wave37. First debug run was red: the histogram test asserted 15 excluded pairs while the independent count is 10 (3+3+2+1+0+0+1); the assertion was corrected and the log overwritten by the rerun. A first negative control swapped two equal outputs (indices 2 and 3, both 1) and could not fail; it now swaps indices 0 and 2. Final: six tests, two debug and two release runs, exit 0 each, sorted named outcomes identical. Source mutation control (`prev[j] + 1` → `prev[j]` in `en::text::lcs`): compiled, five of six tests failed, exit 101; exact restoration verified by hash and a green rerun. Logs: external octopus-wave37-fable-2026-10-31.