# Twenty-one runnable research utilities

The [twenty earlier utilities](PROTOTYPES-2026-10-09-v8.md) now include shared-switch permutation replay, tiny exact laws and seed-support arithmetic. Twenty-three saved component reports contain **2,500 passed checks**: 2,297 earlier plus 176 permutation, 21 entropy and six documentary-contract controls. No full source proof or production sampler was verified.

## Exact finite movement comparison

[kserver_reference.py](tools/kserver_reference.py) accepts a rational metric, initial labeled tuple and fixed request word. It computes an attained offline optimum by conventional DP, replays a witness, and evaluates fixed-label, nearest-label and independent uniform-label policies exactly. It implements no source competitive policy. It rejects nonmetrics and caps eight points, four servers, 64 requests and three million state-label transitions. Budget exhaustion leaves the complete comparison unknown. Dimensions bound frontier/backpointer storage; work units exclude input validation and do not represent bit operations or wall time.

```sh
python3 research/tools/kserver_reference.py research/fixtures/movement-startup-2026-10-09-v1.json
```

[137 checks](snapshots/2026-10-08-baseline/movement-reference-validation-2026-10-09-v1.json) compare complete short label-string enumeration with DP and policy expectations, then check witness replay, horizon distinctions, metrics and budgets. The saved 30-request startup fixture has fixed-label cost 30 and offline optimum 2. This is a small finite control for the source's activation/additive-cost distinction, not performance evidence on a customer workload.

## Exact transport sharpness geometry

[transport_sharpness_reference.py](tools/transport_sharpness_reference.py) reproduces the source's uniform-square three-atom example. It clips rational affine halfplanes, integrates nine map-cell intersections, and compares masses and map norm with analytic formulas. Target W1/W2 use the explicit matching and second-coordinate lower witness; no general transport optimizer runs. It accepts a 256-bit rational parameter 0<a<1/2 and caps 10,000 polygon-vertex examinations. Partial work returns unknown. It proves no arbitrary transport-map or solver guarantee.

```sh
python3 research/tools/transport_sharpness_reference.py research/fixtures/transport-three-atom-2026-10-09-v1.json
```

[131 checks](snapshots/2026-10-08-baseline/transport-reference-validation-2026-10-09-v1.json) cover rational geometry, target metrics, exact half-exponent growth and input/budget boundaries. [Saved examples](snapshots/2026-10-08-baseline/computational-model-examples-2026-10-09-v1.json) include movement comparisons, explicitly conditional activation schedules and transport controls. No source constructor time is measured.

## Documentary and semantic records

The [thirteen-contract registry](prototypes/curated-contracts-2026-10-09-v3.json) adds language-class, uniform k-server and Brenier-map contracts, with [12 checks](snapshots/2026-10-08-baseline/semantic-contract-validation-2026-10-09-v1.json). Complete documentation still grants no applicability/independent-verification certificate and does not verify supplied evidence contents. The [new joined report](prototypes/computational-model-evidence-bundle-2026-10-09-v2/report.md) flags eleven gaps in one self-authored startup claim. It archives all six exact report inputs. Earlier bundles also have separately recovered input archives whose bytes match the original recorded hashes; their original manifests/reports remain preserved. [31 archive checks](snapshots/2026-10-08-baseline/evidence-archive-validation-2026-10-09-v1.json) verify those bytes and historical registry counts without executing the archived tools.

[65 selected definition observations](snapshots/2026-10-08-baseline/definition-hole-review-queue-2026-10-09-v3.json) have no detected intended-model mismatch in this limited review. All ten interfaces in this finite static queue are reviewed at source level; whole imports, proofs and programs remain pending. This is source inspection, not a trusted checker or whole-proof result. [Operational limits](FEASIBILITY-2026-10-09-v5.md).

## Fourier and algebra references

[audit_fourier_aliasing.py](tools/audit_fourier_aliasing.py) compares exact sparse |u|^(p-1)u with centered modulo-grid folding. It uses physical rational coefficients rather than weighted Sobolev coordinates. [110 controls](snapshots/2026-10-08-baseline/fourier-aliasing-validation-2026-10-09-v1.json) include closed cubic formulas, independent direct expansions, complex single-wave formulas, a twelve-dimensional axis fixture and failure limits. [Saved grid-three report](prototypes/fourier-aliasing-grid-3-2026-10-09-v1.json).

```sh
python3 research/tools/audit_fourier_aliasing.py research/fixtures/fourier-aliasing-12d-2026-10-09-v1.json
```

[chromatic_basis_reference.py](tools/chromatic_basis_reference.py) enumerates proper colorings and reconstructs the entire exact finite polynomial after elementary-basis conversion for at most six vertices. An optional supplied nondescent-permutation witness is compared coefficient by coefficient. [106 controls](snapshots/2026-10-08-baseline/chromatic-basis-validation-2026-10-09-v1.json) cover closed formulas, all eligible h through four vertices, paper/Sage examples, witness mutation and budgets. This does not implement the source packet construction or certify its all-r witness. [Algebra dossier](opportunities/039-positive-basis-algebra-audit/2026-10-09-v1.md).

```sh
python3 research/tools/chromatic_basis_reference.py research/fixtures/chromatic-path-three-witness-2026-10-09-v1.json
```

## Prepared ten-claim experiment

[The review packet](prototypes/ten-claim-review-packet-2026-10-09-v1/README.md) contains ten self-authored scenarios, eight intentional scope errors and two synthetic documentary-completeness controls. It preserves source-only/report-assisted cards, a separate self-authored answer key and blank expert results. [25 controls](snapshots/2026-10-08-baseline/ten-claim-packet-validation-2026-10-09-v1.json) check expected code boundaries and exact file pointers for all thirteen contracts. This is a prepared experiment; expert benefit, accuracy and buyer value remain unmeasured. [Enriched registry](prototypes/curated-contracts-2026-10-09-v4.json).

## Queryable permutation reference

[queryable_permutation_reference.py](tools/queryable_permutation_reference.py) has three modes: explicit shared-bit point/inverse replay; exact tiny full permutation laws; and deterministic short-seed support bounds. Missing bits and exhausted law budgets are unknown. [176 switching/law controls](snapshots/2026-10-08-baseline/queryable-permutation-validation-2026-10-09-v1.json) use independent physical all-coin enumeration and materialized/cycle tests. [21 support controls](snapshots/2026-10-08-baseline/permutation-entropy-validation-2026-10-09-v1.json) distinguish statistical full-law guarantees from seeded application goals. [Four-card calibration](prototypes/coordinate-four-card-calibration-2026-10-09-v1.json) does not select a universal sweep count.

```sh
python3 research/tools/queryable_permutation_reference.py research/fixtures/coordinate-sparse-63bit-2026-10-09-v1.json
python3 research/tools/queryable_permutation_reference.py research/fixtures/coordinate-law-d3-L1-m8-2026-10-09-v1.json
python3 research/tools/queryable_permutation_reference.py research/fixtures/permutation-entropy-d30-b256-2026-10-09-v1.json
```

The [fourteen-contract enriched registry](prototypes/curated-contracts-2026-10-09-v5.json) adds source trace-smoothing and shared-randomness obligations, with [six controls](snapshots/2026-10-08-baseline/permutation-contract-validation-2026-10-09-v1.json). A synthetic complete record still verifies no evidence or mathematics. The [new joined report](prototypes/coordinate-permutation-evidence-bundle-2026-10-09-v1/report.md) flags twelve documentary gaps in a self-authored four-sweep seeded claim and archives its six exact inputs. [New application dossier](opportunities/040-queryable-permutation-framework/2026-10-09-v1.md), [SDK specification](plans/queryable-permutation-sdk-2026-10-09-v1.md).

## Full utility directory

| Utility | Capability |
| --- | --- |
| [Proof preflight](tools/proof_preflight.py) | Static module/config/trust metadata |
| [Withdrawal impact](tools/withdrawal_impact.py) | Explicit corrections/dependency paths |
| [Embedding audit](tools/audit_embedding.py) | Finite floating-point distortion |
| [GAD capacity objective](tools/gad_capacity.py) | Finite scalar evaluation |
| [Claim contract audit](tools/audit_claim_contract.py) | Fourteen curated documentary contracts |
| [Periodic interface reference](tools/periodic_interface_reference.py) | Cubic-periodic perimeter formula |
| [Binary waveform audit](tools/audit_binary_waveform.py) | Exact correlations/sample spectrum |
| [Ramanujan graph audit](tools/audit_ramanujan_graph.py) | Exact strict finite spectral bound |
| [Cyclic-chain reference](tools/cyclic_chain_reference.py) | Small-group shortest cyclic quotient chain |
| [Evidence bundle](tools/evidence_bundle.py) | Source fingerprints/joined report |
| [Contingency reference](tools/contingency_reference.py) | Exact bounded table count/rank |
| [Matching certificate audit](tools/audit_matching_certificate.py) | Feasibility/attaining cardinality bound |
| [Existing-solver adapter](tools/solve_and_audit_matching.py) | Bounded proposal/separate audit |
| [Perfect-pairing reference](tools/perfect_matching_reference.py) | Exact count/rank/edge fragility |
| [Switch-chain audit](tools/audit_switch_chain.py) | Exact bounded kernel/law/host calibration |
| [Tree thinness audit](tools/audit_tree_thinness.py) | Exact bounded all-cut ratio/certificate |
| [Movement reference](tools/kserver_reference.py) | Exact bounded offline optimum and named-policy expectations |
| [Transport sharpness reference](tools/transport_sharpness_reference.py) | Exact three-atom polygon/mass/map-distance control |

| [Fourier aliasing reference](tools/audit_fourier_aliasing.py) | Exact sparse odd-power convolution/circular-grid comparison |
| [Chromatic basis reference](tools/chromatic_basis_reference.py) | Exact finite elementary expansion and supplied-witness audit |

| [Queryable permutation reference](tools/queryable_permutation_reference.py) | Shared-bit point/inverse, tiny laws and seeded-support bounds |

Dated validation drivers/output files preserve their earlier editions. Existing successful output paths cannot be reused. Finite checks, syntax/hash consistency and an elapsed work window do not establish broad algorithm superiority, buyer demand or profitability.