# Sixteen runnable research utilities

The [fourteen earlier utilities](PROTOTYPES-2026-10-09-v4.md) now include a bounded exact switch-chain reference and an all-cut tree auditor. The documentary registry has ten curated contracts, with graph kernel/host/time-accounting as the new failure mode. All source proofs and program formal verification remain independently unverified.

## New graph protocol reference

[audit_switch_chain.py](tools/audit_switch_chain.py) enumerates a labeled degree fiber, builds the specified lazy rational kernel, checks row symmetry/laziness and connectivity, and propagates one-start laws exactly. Optional restricted hosts receive no complete-host source guarantee. It caps six vertices, 512 states, 64 steps and two million work units; exhaustion returns unknown. Work units are graph tests, degree updates, proposals and propagation transitions, not bit operations or wall time. It does not implement the unrestricted exact residual sampler.

```sh
python3 research/tools/audit_switch_chain.py research/fixtures/six-cycle-host-switch-2026-10-09-v1.json --steps 12
```

[69 saved checks](snapshots/2026-10-08-baseline/switch-chain-validation-2026-10-09-v1.json) include every four-vertex degree fiber against separate enumeration, a closed-form finite TV law and two model counterexamples. The [saved laws/schedules](snapshots/2026-10-08-baseline/switch-chain-examples-2026-10-09-v1.json) demonstrate restricted-host disconnection and generic accepted-event stationary bias. One-start convergence is not worst-case mixing evidence. The generic jump chain is not a complete audit of an external library.

## New all-cut tree audit

[audit_tree_thinness.py](tools/audit_tree_thinness.py) validates a supplied supported tree and scans every nontrivial cut up to complements. It returns exact connectivity, maximum tree/original-copy ratio, witnesses, the achieved `k*alpha`, and whether a supplied rational target is met. It caps 16 vertices, 256-bit positive multiplicities and five million cut-edge examinations. Multiplicities count distinct original edge copies. The scan is exponential; partial work cannot certify an all-cut target. It constructs no tree or source polynomial backend.

```sh
python3 research/tools/audit_tree_thinness.py research/fixtures/k4-path-thinness-2026-10-09-v1.json
```

[30 saved checks](snapshots/2026-10-08-baseline/tree-thinness-validation-2026-10-09-v1.json) cover all 16 K4 trees, exact targets, copy scaling, `2^100` binary copies, invalid trees and budget semantics. The [K4 path example](snapshots/2026-10-08-baseline/tree-thinness-examples-2026-10-09-v1.json) has fundamental-cut maximum `1/3` but true all-cut ratio `3/4`.

## Shared documentary evidence

The [ten-contract registry](prototypes/curated-contracts-2026-10-09-v2.json) adds eight [linter checks](snapshots/2026-10-08-baseline/chain-contract-validation-2026-10-09-v1.json). A complete manifest still grants no mathematical applicability or independently verified label. The [new graph-chain report](prototypes/graph-chain-evidence-bundle-2026-10-09-v1/report.md) joins source hashes/static metadata with one self-authored restricted-host claim, flagging nine documentary gaps. It is not an external product claim or ten-claim expert benchmark. The older evidence bundle preserves its nine-contract edition.

## 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) | Ten 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 |

Thirteen saved component reports contain 1,745 passed checks: the prior 1,638 plus 69 switch-chain, 30 thinness and eight contract checks. These finite records do not prove the source results, broad algorithm superiority, buyer demand or profitability. Dated drivers/output paths preserve earlier editions and cannot be rerun into existing files. [Construction limits](FEASIBILITY-2026-10-09-v4.md).