--- title: "algorithm-composition-wave11 — Mova code model" description: "Mova code model of algorithms/tests/composition_wave11.rs: components with their labels, obernants and the model text." url: "https://groupants.elamur.ai/free/en/mova/algorithms/tests/composition_wave11.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: # algorithm-composition-wave11 The groupant beside algorithms/tests/composition_wave11.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 instance - **source:** [`algorithms/tests/composition_wave11.rs`](https://github.com/ElamurAI/mova-free/blob/main/algorithms/tests/composition_wave11.rs) - **source SHA-256:** `c7d3f12a013c9e75…` - **repository folder:** [`algorithms/tests/composition_wave11.rs.groupant`](https://github.com/ElamurAI/mova-free/tree/main/algorithms/tests/composition_wave11.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 | [forward](#forward) | | **ast** | partial | `syntax.json` | | **cost** | symbolic unmeasured | [cost](#cost) | | **descriptant** | present | [epoch-memory](#epoch-memory) | | **invariant** | partial | [invariant](#invariant) | | **tests** | existing checks referenced | [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 | |---|---|---|---| | `behavior_complement` | behavior_complement | partial source derived | [behavior_complement](#behavior-complement) | | `reverse_reconstruction` | reverse_reconstruction | partial source derived | [reverse_reconstruction](#reverse-reconstruction) | | `matching-unit-flow` | capacity_matching_embedding | partial source derived | [matching-unit-flow](#matching-unit-flow) | | `lowlink-reachability` | canonical_partition_relation | partial source derived | [lowlink-reachability](#lowlink-reachability) | | `unrestricted-edit-bounds` | edit_objective_inclusion | partial source derived | [unrestricted-edit-bounds](#unrestricted-edit-bounds) | | `palindrome-occurrence` | occurrence_projection_identity | partial source derived | [palindrome-occurrence](#palindrome-occurrence) | | `lyndon-rotation` | rotation_quotient_reconstruction | partial source derived | [lyndon-rotation](#lyndon-rotation) | | `recurrence-prefix` | finite_prefix_continuation | partial source derived | [recurrence-prefix](#recurrence-prefix) | | `no-carry-convolution` | disjoint_bit_embedding | partial source derived | [no-carry-convolution](#no-carry-convolution) | | `assignment-cycle-relaxation` | objective_relaxation_certificate | partial source derived | [assignment-cycle-relaxation](#assignment-cycle-relaxation) | ## Model text ### model ## Native eighty-algorithm joins ### forward Eight supplied-input API joins retain identities across exact algorithms. Each has its own domain; this is not one serial runtime pipeline. ### invariant Preserve vertices, original edge indices, bytes, item multiplicity, witness coordinates, coefficient order and modulus. Leaf resource/error domains apply before comparison. ### cost Sum reached calls and explicit oracle adapters. Enumeration/reference work can dominate; no library or school speedup follows. Per-view fixture bounds follow below. ### epoch-memory 2026-10-30: eight joins supplement independent leaf oracles. No-carry coefficient positioning is a compiled adapter control. Syntax is partial; macro bodies opaque. No general proof or automatic substitution. ### behavior_complement Type: behavior_complement. Within tagged supplied-input domains exclude lost vertex/edge identity, invalid flow certificates, conflated edit objectives, conflated palindrome counts, changed rotation bytes, mixed recurrence coefficients/moduli and omitted cycle constraints. This models U minus the declared relation, not a complement of sampled successes. Leaf allocation/error assumptions remain; Pass requires executed assertions. ### reverse_reconstruction Type: reverse_reconstruction. Retain compatible inputs and intermediate observations. Flow values, SCCs, edit distances and palindrome summaries have many preimages. Minimum rotation loses the original rotation offset; finite recurrence prefixes do not determine arbitrary future sequences. Assignment objectives can correspond to disconnected cycle covers. No unique global inverse follows. ### matching-unit-flow Type: capacity_matching_embedding. All 512 three-by-three bipartite graphs, with selected duplicated adjacency, become a shared unit-capacity source/left/right/sink network. HK and the earlier matcher agree in cardinality; Dinic and Edmonds-Karp agree with it. Original edge flows respect capacity/conservation and their source-side cut sums to the same value. Witnesses may differ. Include construction plus reached solver/certificate costs. ### lowlink-reachability Type: canonical_partition_relation. For all 512 directed three-vertex graphs including loops, Tarjan and the existing SCC API return the same canonical partition. Shared vertex ownership equals mutual reachability in the reflexive closure. Canonical sorting is additional presentation cost, not part of a blanket linear-time claim. The partition cannot reconstruct graph edges. ### unrestricted-edit-bounds Type: edit_objective_inclusion. For 225 binary-word pairs through length three, unrestricted Damerau distance is at most OSA, which is at most Levenshtein; symmetry is checked. CA to ABC distinguishes unrestricted distance 2 from OSA 3. The relation follows permitted-script inclusion, not equality of objectives. Byte units and leaf resource limits remain. ### palindrome-occurrence Type: occurrence_projection_identity. For 255 binary words through length seven, summed Eertree occurrence counts equal sum(Manacher odd+even radii), and maximum lengths agree. Returned Eertree ranges are palindromes at original byte coordinates. This parent check does not compare every individual occurrence count or longest-tie identity; independent leaf oracles carry those obligations. ### lyndon-rotation Type: rotation_quotient_reconstruction. For 255 binary words, factor ranges reconstruct the original bytes in nonincreasing factor order. The last doubled-text Lyndon factor starting before n gives a minimum rotation; compare its bytes with inverse(BWT-column,primary 0). Periodic offsets can differ while bytes agree. Empty text has an explicit case. Cost includes complete validated BWT inverse, not merely linear Duval. ### recurrence-prefix Type: finite_prefix_continuation. Four known generated recurrences of order at most three supply twelve prefix terms; BM coefficients feed Kitamasa with the same prime and lag order, reproducing 32 generated terms. Empty inferred order is handled as zero only in the known-zero fixture. Arbitrary finite prefixes admit other futures; this is not prediction of arbitrary unseen data. ### no-carry-convolution Type: disjoint_bit_embedding. Across 32 supplied coefficient fixtures, support of A uses low two index bits and support of B uses disjoint high bits. Thus i+j=i XOR j and all sums are below 16: FWHT output equals the NTT low coefficients and higher coefficients vanish. A separate overlap example differs at indices 0 and 2. A compiled wrong-position adapter breaks the premise and must fail. This is not unrestricted convolution equivalence. ### assignment-cycle-relaxation Type: objective_relaxation_certificate. 64 complete directed fixtures use n=2..5, edge costs 0..8 and diagonal 9n+1. A valid cycle costs at most 8n, so the assignment optimum avoids diagonal and supplies a cycle-cover lower bound on Held-Karp. Check original-coordinate cost, feasible dual equality and tour witness. If assignment is one cycle, objectives agree; multiple cycles need not. Missing arcs and arbitrary diagonal penalties lie outside this adapter. ### evidence #### Executed integration evidence, 2026-10-30 Eight native joins pass twice in debug and twice in release within the full 382-unit/38-integration/one-doctest suite. Sorted named outcomes match across all four executions. Strict all-target algorithms Clippy and crate formatting pass. The compiled b[4*i] to b[3*i] adapter fails no_carry_support_embeds_xor_in_polynomial_convolution at an equality assertion; exact bytes are restored before positive repeats. Final syntax projections repeat identically. Fixture domains, inverse ambiguity and incomplete observations are specified in model.md. These checks establish neither a general proof nor automatic production substitution. Root receipt set: octopus-wave11-integration-2026-10-30. 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