---
title: "algorithm-composition-wave25 — Mova code model"
description: "Mova code model of algorithms/tests/composition_wave25.rs: components with their labels, obernants and the model text."
url: "https://groupants.elamur.ai/free/en/mova/algorithms/tests/composition_wave25.rs.groupant/"
---
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# algorithm-composition-wave25

The groupant beside algorithms/tests/composition_wave25.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 descriptive instance
- **source:** [`algorithms/tests/composition_wave25.rs`](https://github.com/ElamurAI/mova-free/blob/main/algorithms/tests/composition_wave25.rs)
- **source SHA-256:** `716553074fe8c5b7…`
- **repository folder:** [`algorithms/tests/composition_wave25.rs.groupant`](https://github.com/ElamurAI/mova-free/tree/main/algorithms/tests/composition_wave25.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 | [approximant](#approximant) |
| **ast** | partial | `syntax.json` |
| **descriptant** | present | [descriptant](#descriptant) |
| **invariant** | partial | [approximant](#approximant) |
| **tests** | existing checks referenced | [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) |
| `diagonal_stationarity_join` | diagonal_stationarity_join | partial source derived model | [diagonal_stationarity_join](#diagonal-stationarity-join) |
| `lasso_soft_threshold_join` | lasso_soft_threshold_join | partial source derived model | [lasso_soft_threshold_join](#lasso-soft-threshold-join) |
| `reduction_reachability_rejects_dominator_transfer` | reduction_reachability_rejects_dominator_transfer | partial source derived model | [reduction_reachability_rejects_dominator_transfer](#reduction-reachability-rejects-dominator-transfer) |
| `unit_flow_bfs_join` | unit_flow_bfs_join | partial source derived model | [unit_flow_bfs_join](#unit-flow-bfs-join) |
| `clique_order_core_coordinates_join` | clique_order_core_coordinates_join | partial source derived model | [clique_order_core_coordinates_join](#clique-order-core-coordinates-join) |
| `interpolation_polynomial_and_spline_affine_join` | interpolation_polynomial_and_spline_affine_join | partial source derived model | [interpolation_polynomial_and_spline_affine_join](#interpolation-polynomial-and-spline-affine-join) |
| `quadrature_analytic_join` | quadrature_analytic_join | partial source derived model | [quadrature_analytic_join](#quadrature-analytic-join) |
| `fft_exact_field_fixture_join` | fft_exact_field_fixture_join | partial source derived model | [fft_exact_field_fixture_join](#fft-exact-field-fixture-join) |
| `subset_triangular_reconstruction_rejects_or_join` | subset_triangular_reconstruction_rejects_or_join | partial source derived model | [subset_triangular_reconstruction_rejects_or_join](#subset-triangular-reconstruction-rejects-or-join) |
| `discrete_log_target_join` | discrete_log_target_join | partial source derived model | [discrete_log_target_join](#discrete-log-target-join) |
| `bpe_codec_model_bound_join` | bpe_codec_model_bound_join | partial source derived model | [bpe_codec_model_bound_join](#bpe-codec-model-bound-join) |
| `patience_myers_edit_observations_join` | patience_myers_edit_observations_join | partial source derived model | [patience_myers_edit_observations_join](#patience-myers-edit-observations-join) |

## Model text


### descriptant

#### Wave25 composition witnesses

##### Prospective epoch

#### Wave25 prospective integration — 2026-10-30

Base fd540f37badaad97b53d56ba81684bbbc2ca4b9b. Add 25 modules in five families: accelerated/spectral quadratic and proximal LASSO optimization; graph flow/order/core/dominator/reduction; interpolation/quadrature; field/complex algebra; byte editing/compression. Implementation and tests form separate leaves. Five family groups describe tagged observations, not one serial pipeline. Root plans twelve independent composition checks plus production Mova refinement.

Joins: diagonal optimizers share b/d and stationarity but not trajectories; LASSO shares soft-threshold solutions on identity design. DAG reduction preserves reachability but can CHANGE dominators (0->1,0->2,1->2); reduction before dominance is a rejected transfer. Unit-flow paths share BFS distance on admitted unit-cost DAGs. Clique ordering/core observations retain vertex coordinates without proving general chordality. Polynomial interpolation agrees on a common polynomial domain; natural splines share affine fixtures. Quadratures share known integrals but difference estimates are not universal error bounds. FFT convolution matches exact field products only on small safely representable fixtures. Subset convolution uses disjoint union, unlike OR/zeta multiplication; a triangular field system reconstructs an operand when the empty-set coefficient is invertible. BSGS reproduces modular targets with least-exponent/zero-base conventions. BPE token bytes compose with codecs only with the same model and bounds. Patience patches reconstruct targets but need not minimize edits; Myers agrees with exact edit distance on admitted width.

Mova: conversion checking uses memoized functional-graph traversal and one byte-color vector for n>64, retaining successors and first error (two total allocations with parsed heads); tiny walks remain. This revises the initial in-place sentinel idea before implementation to avoid lost-link ambiguity. Spatial scans specialize processing; index construction waits until four whole-fact frontier scans are spent, bounding pre-index work by 4F. Retain fact order, inverse edges, product state and absent intermediate IDs. Compare fd540 parent and original legacy where available. No threshold fitting on confirmation. These are predictions, not gains.

Repeated debug/release native checks, bounded independent/exhaustive oracles, compiled semantic mutants, paired syntax, formatting/Clippy and structural/catalog controls. Serial benchmarks after workers stop, warmups/alternating order; preserve regressions. No live teacher, corpus/database mutation, GPU/full-school/held-out run. No universal percentage guarantee or proof from registration or finite checks.


##### Mathematical combiner

Source-bound syntax projects the harness. Its forward model is conjunction of the twelve adapter/observation predicates; typed views describe excluded outcomes and ambiguous preimages. Constituent definitions and literature remain in their production modules; independent test identities include monomial antiderivatives, diagonal stationary points and exact integer convolution. Leaf children=[] here; parent registry models cross-file wiring and bindings. Raw Rust remains authoritative; syntax lacks semantic resolution/macro expansion.

##### Observed epoch 2026-10-30

Twelve tests pass twice debug and twice Cargo release; normalized names/outcomes identical. A compiled u16 little-endian decode to big-endian mutant fails bpe_codec_model_bound_join token equality; original bytes restored and positives rerun. Strict targeted Clippy passes. No benchmark or broad accuracy/speed claim. Rejected transfers: DAG reduction changes dominators; OR convolution is not disjoint subset convolution; patience edit counts are not Levenshtein minima.

### model

### behavior_complement

Let J map fixed admitted fixtures and the linked production implementations to twelve assertion outcomes. Its complement contains a Pass paired with any violated assertion: changed vertex coordinates, lost u16 high bytes, wrong product index, flow imbalance, invalid solver status, or error outside stated tolerance. A valid constituent output is insufficient if an adapter changes its meaning. Passing all fixtures excludes these observed mismatches only; it does not exclude every untested composition bug.

### reverse_reconstruction

Pass identifies the intersection of twelve finite observational equivalence classes, not unique implementations or inputs. Optimizers with distinct iteration trajectories share stationary solutions; zero and an unsampled bump can share quadrature output; multiple DAG edge sets share reachability; codec tokenizations differ while decoded bytes agree. Output agreement cannot recover discarded path structure, intermediate iterates, unsampled function values, or encoder choices.

### diagonal_stationarity_join

Join heavy-ball, Nesterov and BB reports on d=[1,3,9], b=[2,-3,4.5], initial zero, tolerance 1e-9 and cap1000. All Converged x approximate b/d within1e-8, independently recomputed Euclidean gradient norm matches report within1e-14. This projection forgets trajectories and iteration count; equal optima do not imply equal iteration histories or speed.

### lasso_soft_threshold_join

For identity3 design and b=[3,-2,.25], lambda=.5, ISTA and FISTA converge to scalar soft-threshold oracle [2.5,-1.5,0]. Recompute .5||x-b||²+.5||x||1 and compare reported objective within1e-12. Identity admits this closed form; applying it to arbitrary correlated designs is excluded. KKT residual and coordinate error remain distinct metrics.

### reduction_reachability_rejects_dominator_transfer

For all64 labelled increasing-edge DAGs on4 vertices, BFS reachability support is identical before/after reduction for each source; distances are deliberately not compared. Triangle 0->1,0->2,1->2 has dom(2)=[0,2], but reduced chain gives [0,1,2]. Thus reachability quotient has multiple dominance preimages and reduction-before-dominance is rejected.

### unit_flow_bfs_join

For all64 increasing-edge DAGs on4 vertices, assign capacity1/cost1 to each edge and limit1 from0 to3. If BFS distance exists flow.value=1 and cost=distance, otherwise both0. Per-edge capacities and per-vertex signed balances are checked. This equivalence depends on unit costs, one unit demand and admitted acyclic graph; negative cycles and general capacities/costs are not transferred.

### clique_order_core_coordinates_join

On complete simple graphs sizes1..8, smallest-ID tie MCS returns0..n and (n-1)-core is all vertices; n-core empty. Coordinates retained unchanged. Four-cycle also returns an MCS order and full2-core but has neither diagonal, so these shared observations do not certify chordality. Several nonisomorphic graphs can share order/core outputs.

### interpolation_polynomial_and_spline_affine_join

On nodes[-2,-.5,1,3], Neville and Newton match q^d for d0..3 at21 quarter-grid queries in domain. Natural spline agrees only on affine2q+1 using same nodes. Global cubic interpolation is not equated to natural spline for general degree3; natural boundary curvature constrains a different problem. Scalar queries have ambiguous polynomial preimages.

### quadrature_analytic_join

Trapezoid tolerance1e-8/cap100000 and tanh-sinh tolerance1e-10/cap10000 integrate powers0..3 on[0,1]. Require EstimatedTolerance and compare independently to1/(d+1) with absolute tolerances2e-8 and1e-10. This finite observation provides no arbitrary callback accuracy bound; difference estimators miss unsampled spikes and tanh-sinh fixed-window tails.

### fft_exact_field_fixture_join

For lengths1,3,17 and bounded integer coefficient patterns mod5/mod3, zero-pad to next power2; FFT negative-phase, complex pointwise multiplication, inverse normalization, then truncate to a.len+b.len-1. Compare against Karatsuba field product and independent double-loop integer convolution, all below field modulus and safely small f64 integers. Imaginary residual <=1e-8 and real error <=1e-8. Modular wrap and large coefficients are excluded from transfer.

### subset_triangular_reconstruction_rejects_or_join

For length8 a[empty]=2, h=a*b disjoint subset convolution. Build matrix M[S,T]=a[S xor T] if T subset S else0; field solve uniquely recovers b and has empty nullspace since diagonal a[empty] invertible. Direct OR product for [0,1] with itself is[0,1], whereas disjoint convolution is[0,0]; ranked subset convolution cannot be replaced by ordinary zeta/OR multiplication. Zero empty coefficient removes this uniqueness premise.

### discrete_log_target_join

Targets 3^e mod998244353 for e in{0,1,2,7,31} feed BSGS; recovered exponent equals e, modular re-power matches target and bounded earlier exponent scan finds no earlier solution. Explicit conventions0^0=1 and discrete_log(0,0)=1; base1,target2 has no solution. Modular exponent map has many preimages globally; the least-exponent contract selects one.

### bpe_codec_model_bound_join

Train BPE on repeated-byte fixture, require some token>255, serialize each u16 little-endian, LZ77/LZW roundtrip bytes, recover exact u16 sequence, then decode with the identical BPE model and output bound. Too-small output cap rejects; empty unrelated model rejects high tokens. Model identity is essential: a different compatible model may decode valid tokens differently, so this is not authentication. Endian-adapter mutant compiles and fails token equality.

### patience_myers_edit_observations_join

Four admitted byte pairs: patience patch reconstructs target at exact cap; Myers global distance agrees with scalar Levenshtein production DP, and number of non-Equal patience edits >= distance. abc->axc gives2 insert/delete edits vs Levenshtein1 substitution. Patch correctness does not imply minimality under a different edit operation set; width is within64 and byte rather than Unicode coordinates retained.

### approximant

#### Forward and invariant

Twelve bounded cross-module composition checks with independent analytic/exhaustive fixture observations, retaining explicit rejected transfers.

J=AND(J1,...,J12), each Ji is the named finite observation in model.md. Every adapter retains vertex IDs, coefficient order, field modulus, byte/token widths and function-domain premises. A constituent's success cannot silently turn into an absent or zero result. No aggregate numerical percentage guarantee follows from conjunction.

Bounded harness: two64-DAG enumerations on4 vertices; cliques1..8; 3-dimensional optimizers capped1000; 21 query points; quadrature calls capped100000/10000; FFT max64; subset solve8x8; five nontrivial fixed-prime BSGS calls with <=31596 baby entries; byte fixtures <64. Sum of child work, not a serial production pipeline; allocation/panic semantics inherited.

No executable surrogate: assertions and categorical adapter validity do not have a useful approximate replacement metric. Unsupported profile, not zero-error speed claim.

### tests

Run cargo test -p mova-algorithms --test composition_wave25 and release equivalent. Twelve named tests correspond one-to-one with specialized models. Receipts: $MOVA_DATA/runs/octopus-wave25-numerical-2026-10-30/composition-*.log. Mutation: bytes_tokens from_le_bytes -> from_be_bytes must compile and fail bpe_codec_model_bound_join; restore and rerun. Finite successes are not general proofs.