# Thirty-eight runnable research utilities

Sixty-one saved component reports contain **29,924 passed checks**. The browser release adds 119 controls and an interface to the existing facility module; it is not counted as another utility.

## Complete utility directory

| Utility | What it does | Material boundary |
| --- | --- | --- |
| [proof_preflight.py](tools/proof_preflight.py) | Inspect selected formal configuration/module metadata | Static presence/trust settings, no proof execution |
| [withdrawal_impact.py](tools/withdrawal_impact.py) | Record explicit withdrawals and dependencies | Three notices/two explicit edges; not a full theorem graph |
| [audit_embedding.py](tools/audit_embedding.py) | Check finite embedding quantities | Sampled/finite floating calculation, no universal guarantee |
| [gad_capacity.py](tools/gad_capacity.py) | Evaluate scalar generalized-amplitude-damping expression | Numerical convention/optimization, no hardware or finite decoder certificate |
| [audit_claim_contract.py](tools/audit_claim_contract.py) | Lint documentary source/model obligations | Twenty-one curated contracts; supplied statuses and evidence contents unverified |
| [periodic_interface_reference.py](tools/periodic_interface_reference.py) | Periodic interface formula reference | Specified finite geometry, no general optimizer |
| [audit_binary_waveform.py](tools/audit_binary_waveform.py) | Exact finite correlation and sampled spectrum | No full channel or physical waveform certification |
| [audit_ramanujan_graph.py](tools/audit_ramanujan_graph.py) | Rational contrast-space spectral acceptance | Supplied finite graph, not source constructor |
| [cyclic_chain_reference.py](tools/cyclic_chain_reference.py) | Tiny group cyclic-chain enumeration | At most sixteen elements, no effective spectrum witness |
| [evidence_bundle.py](tools/evidence_bundle.py) | Join source hashes/static metadata/claim audit | Archives six exact inputs; no source/proof execution |
| [contingency_reference.py](tools/contingency_reference.py) | Exact bounded table count/rank/unrank/law | Dimension six/total128; conventional DP, not source sampler |
| [audit_matching_certificate.py](tools/audit_matching_certificate.py) | Check matching and attaining cardinality bound | Exact supplied witness/bound, no extra allocation constraints |
| [solve_and_audit_matching.py](tools/solve_and_audit_matching.py) | Existing NetworkX proposal plus separate audit | Unit cardinality model, no source accelerated matcher |
| [perfect_matching_reference.py](tools/perfect_matching_reference.py) | Tiny exact counts/ranks/edge fragility | At most24 vertices, no FPRAS |
| [audit_switch_chain.py](tools/audit_switch_chain.py) | Exact tiny specified-kernel TV | At most6 vertices/512 states/64 steps; complete-host model |
| [audit_tree_thinness.py](tools/audit_tree_thinness.py) | Exact all-cut finite tree audit | At most16 vertices; not broad thin-tree construction |
| [kserver_reference.py](tools/kserver_reference.py) | Rational offline optimum and named-policy replay | At most8 points/4 servers/64 requests; no source online policy |
| [transport_sharpness_reference.py](tools/transport_sharpness_reference.py) | Exact three-atom rational geometry | Uniform-square example, no arbitrary transport solver |
| [audit_fourier_aliasing.py](tools/audit_fourier_aliasing.py) | Sparse exact odd-power convolution/grid folding | Typed support/work/bit caps; no PDE solution certificate |
| [chromatic_basis_reference.py](tools/chromatic_basis_reference.py) | Tiny exact chromatic/e-basis reconstruction | At most6 vertices; not broad packet/witness theorem implementation |
| [queryable_permutation_reference.py](tools/queryable_permutation_reference.py) | Shared-switch point/inverse replay and tiny laws | Explicit bits/dyadic domain, no universal mixing constant |
| [permutation_provider_reference.py](tools/permutation_provider_reference.py) | Decimal-wire seeded or locked local stored bits | Distinct randomness models; capped append-only JSON store |
| [palindrome_minorant_reference.py](tools/palindrome_minorant_reference.py) | Exact tiny palindrome law/operator calibration | Two/four slots; no universal numerical P |
| [audit_contingency_law.py](tools/audit_contingency_law.py) | Complete finite law and fixed-event comparison | Explicit conditioning, at most2,000 tables, unknown on exhaustion |
| [bounded_flow_reference.py](tools/bounded_flow_reference.py) | Signed-bound private-vertex flow reduction/counts | Tiny exact table engine; no unrestricted FPRAS/sampler |
| [three_machine_reference.py](tools/three_machine_reference.py) | Unit-job schedule audit/exact tiny optimum/deadline evidence | At most18 jobs/50,000 states/2m transitions; exponential |
| [solve_and_audit_three_machine.py](tools/solve_and_audit_three_machine.py) | Existing CP-SAT proposal and finite independent evidence | Same strict unit model; solver status distinct from independent optimum |
| [subset_sum_reference.py](tools/subset_sum_reference.py) | Exact disjoint-half support/multiplicity/witness reference | Two–64 positive identified items; 50k sum records/2m generation/probe work, not source backend |
| [subset_sum_schedule.py](tools/subset_sum_schedule.py) | Exact known guards and conditional decision-error/amplification algebra | Fixed main cutoffs unselected; source implementations and independence unvalidated |
| [solve_and_audit_subset_sum.py](tools/solve_and_audit_subset_sum.py) | Existing integer CP-SAT proposal and original-ID witness evidence | Deliberate total/target cap 2^62-1; solver satisfaction status does not give uniqueness/count |
| [superstring_packaging_reference.py](tools/superstring_packaging_reference.py) | Emit indexed immutable byte-view artifacts and compare complete compressed bytes | At most128 records/16KiB literal bytes; exact DP at most 12 reduced strings; no source factor-two backend |
| [superstring_counts_reference.py](tools/superstring_counts_reference.py) | Bounded paper forced-count recursion and balanced base graph | Reduced length 128/512 substrings/2m charges; no full layer/request/cycle construction or proof acceptance |
| [numerical_range_polynomial_reference.py](tools/numerical_range_polynomial_reference.py) | Exact finite norm threshold, PSD support halfspaces and covered polynomial upper bounds | n≤8/m≤4/degree≤6; new constant two conditional, exact inputs and capped arithmetic only |
| [metric_facility_reference.py](tools/metric_facility_reference.py) | Strict metric, exact plan/LP-dual audit and bounded k-median enumeration | At most 48 locations, unweighted and uncapacitated; no source backend or physical-data bridge |
| [noncommutative_hitting_reference.py](tools/noncommutative_hitting_reference.py) | Exact ordered rational matrix witnesses via source-derived structured actions | Visible division-free tree; nonzero refutes a free identity, zero remains conditional/unknown; explicit bit/work/dimension caps |
| [mean_payoff_label_reference.py](tools/mean_payoff_label_reference.py) | Bounded deterministic source recursion and separate threshold-region strategy checker | Ordinary signed-edge deterministic model; unknown on limits, completed labels source-conditional; no value-optimality or companion claim |
| [facility_review_workbench.py](tools/facility_review_workbench.py) | Stable-ID CSV import, exact model/plan review, optional OR-Tools and preserved HTML/JSON exports | Local strict/unweighted/uncapacitated model; no hosted uploads, automatic general duals or validated customer value |
| [facility_assignment_audit.py](tools/facility_assignment_audit.py) | Exact weighted rectangular plan/capacity audit, optional existing solver and preserved HTML/JSON reports | Whole-client assignment, 512 clients/128 sites; no source-theorem extension, geographic validation or hosted uploads |

All dated validators/publishers and archived historical copies are supporting tooling, not additional utilities. The [preceding prototype edition](PROTOTYPES-2026-10-09-v23.md) preserves detailed earlier measurements and controls.

## Local browser interface

[Facility Plan Auditor](https://mathideas.stera.ventures/facility/) selects and reviews six files on the user's device. It checks exact costs, identities, mandatory sites and whole-client capacities; it does not run an optimization solver. [Release evidence](prototypes/facility-browser-2026-10-09-v1/report.md) includes 65 Python parity cases and a grouped 7,776-model/93,312-plan independent grid among 119 controls. The grouped grid adds one component check to avoid treating every plan as a separate test.

Actual file selection and fractional calculations were inspected. Original bytes, input hashes and engine identity are included in HTML/JSON exports. In-app native download and OS clipboard completion remain unverified; complete text exports are visible as a fallback. The previous edition preserves earlier utility measurements. No customer value, source theorem extension or formal program proof is claimed.