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Thirty runnable research utilities
Thirty-nine saved component reports contain 10,185 passed checks. The preceding edition had 7,727 checks; this continuation adds 2,294 subset-sum reference/guard/error controls, 150 live existing-solver controls and 14 documentary registry controls. These are finite reference, integration and metadata checks, with no source-proof, unrestricted backend, actual reconciliation-model or business certification.
Complete utility directory
| Utility | What it does | Material boundary |
|---|---|---|
| proof_preflight.py | Inspect selected formal configuration/module metadata | Static presence/trust settings, no proof execution |
| withdrawal_impact.py | Record explicit withdrawals and dependencies | Three notices/two explicit edges; not a full theorem graph |
| audit_embedding.py | Check finite embedding quantities | Sampled/finite floating calculation, no universal guarantee |
| gad_capacity.py | Evaluate scalar generalized-amplitude-damping expression | Numerical convention/optimization, no hardware or finite decoder certificate |
| audit_claim_contract.py | Lint documentary source/model obligations | Eighteen curated contracts; supplied statuses and evidence contents unverified |
| periodic_interface_reference.py | Periodic interface formula reference | Specified finite geometry, no general optimizer |
| audit_binary_waveform.py | Exact finite correlation and sampled spectrum | No full channel or physical waveform certification |
| audit_ramanujan_graph.py | Rational contrast-space spectral acceptance | Supplied finite graph, not source constructor |
| cyclic_chain_reference.py | Tiny group cyclic-chain enumeration | At most sixteen elements, no effective spectrum witness |
| evidence_bundle.py | Join source hashes/static metadata/claim audit | Archives six exact inputs; no source/proof execution |
| contingency_reference.py | Exact bounded table count/rank/unrank/law | Dimension six/total128; conventional DP, not source sampler |
| audit_matching_certificate.py | Check matching and attaining cardinality bound | Exact supplied witness/bound, no extra allocation constraints |
| solve_and_audit_matching.py | Existing NetworkX proposal plus separate audit | Unit cardinality model, no source accelerated matcher |
| perfect_matching_reference.py | Tiny exact counts/ranks/edge fragility | At most24 vertices, no FPRAS |
| audit_switch_chain.py | Exact tiny specified-kernel TV | At most6 vertices/512 states/64 steps; complete-host model |
| audit_tree_thinness.py | Exact all-cut finite tree audit | At most16 vertices; not broad thin-tree construction |
| 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 | Exact three-atom rational geometry | Uniform-square example, no arbitrary transport solver |
| audit_fourier_aliasing.py | Sparse exact odd-power convolution/grid folding | Typed support/work/bit caps; no PDE solution certificate |
| chromatic_basis_reference.py | Tiny exact chromatic/e-basis reconstruction | At most6 vertices; not broad packet/witness theorem implementation |
| queryable_permutation_reference.py | Shared-switch point/inverse replay and tiny laws | Explicit bits/dyadic domain, no universal mixing constant |
| permutation_provider_reference.py | Decimal-wire seeded or locked local stored bits | Distinct randomness models; capped append-only JSON store |
| palindrome_minorant_reference.py | Exact tiny palindrome law/operator calibration | Two/four slots; no universal numerical P |
| audit_contingency_law.py | Complete finite law and fixed-event comparison | Explicit conditioning, at most2,000 tables, unknown on exhaustion |
| bounded_flow_reference.py | Signed-bound private-vertex flow reduction/counts | Tiny exact table engine; no unrestricted FPRAS/sampler |
| 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 | Existing CP-SAT proposal and finite independent evidence | Same strict unit model; solver status distinct from independent optimum |
| 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 | Exact known guards and conditional decision-error/amplification algebra | Fixed main cutoffs unselected; source implementations and independence unvalidated |
| 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 |
All dated validators/publishers and archived historical copies are supporting tooling, not additional utilities. The preceding prototype edition preserves detailed earlier measurements and controls.
Newly completed statistical integration
586 live SciPy controls compare the exact reference with SciPy 1.18.1/NumPy 2.5.3 on 284 two-by-two margin pairs and 494 observed tables, plus five public/generated cases. A working fresh environment was created without modifying the default or first failed fresh 1.15.3 environment. R remains unexecuted. Floating agreement is finite and tolerance-bounded, not an exact library proof or design validation. Runtime and source hashes, public law report.
python3 research/tools/audit_contingency_law.py research/fixtures/contingency-scipy-fisher-threshold-2026-10-09-v1.json
The declared probability-order event is held fixed. Conditional-independence probability 5/143 versus uniform-table probability 3/7 crosses the declared 1/20 threshold because the law changes. Bounds use explicit renormalization of the original law; they do not automatically model real structural zeros. No large-support or source-backend performance was measured.
New scheduling references
3,346 finite controls compare all 1,099 topologically ordered DAG edge sets through five jobs with a separate backtracking slot-variable oracle. The reference validates explicit model fields, job identities and acyclicity; checks capacities/strict precedence; computes elementary lower/checked upper bounds; and completes ideal-state BFS when needed. Empty, oversized, cyclic and mismatched inputs are refused. Budget exhaustion grants no exact optimum. Independently sufficient deadline evidence can survive exhaustion.
python3 research/tools/three_machine_reference.py research/fixtures/three-machine-greedy-counterexample-2026-10-09-v1.json
python3 research/tools/three_machine_reference.py research/fixtures/three-machine-sync-bottleneck-2026-10-09-v1.json --state-budget 1
The generated nine-job case has a four-slot priority heuristic versus optimum three. The six-job case has elementary lower bound two versus optimum three. A valid schedule alone is not an optimality certificate; a valid schedule attaining the elementary lower bound can be one for the finite model. The source exponent 150020 and fixed-machine proof are not implemented by this exponential search.
40 live CP-SAT controls compare eight generated models with OR-Tools 9.15.6755, retaining separately checked schedules and tiny optima. Runs with one worker and a two-second limit already reach those optima, so no new solver advantage is shown. A FEASIBLE proposal attains the capacity bound in the independent-18 case. The exhausted independent six-job control does not inherit its solver's OPTIMAL status. Saved comparison, wheel installation report.
/tmp/openai-math-scheduling-20261009-FKmLBr/bin/python3 research/tools/solve_and_audit_three_machine.py research/fixtures/three-machine-greedy-counterexample-2026-10-09-v1.json
That interpreter is the preserved environment for this run; the saved report records packages/runtime. No existing installation was altered. Times are diagnostic single runs, not a benchmark or deployment guarantee. Current scheduling dossier.
Subset-sum reference and existing-engine evidence
2,294 controls compare 28,404 method/target queries across all 1,089 positive value words 1..3 through six items with a separate binary-choice count oracle. Both exact reference methods preserve original-index multiplicity. Additional controls check invalid models/IDs, 256-bit exact arithmetic, guards, budget states and conditional majority-error algebra.
python3 research/tools/subset_sum_reference.py research/fixtures/subset-sum-repeated-64-2026-10-09-v1.json
python3 research/tools/subset_sum_reference.py research/fixtures/subset-sum-repeated-64-2026-10-09-v1.json --method occurrence_MITM
The 64-one target-32 generated case uses 98 peak sum records under compressed support and retains C(64,32)=1,832,624,140,942,590,534 distinct indexed solutions. The occurrence method exhausts 50,000 records and returns unknown. These record/work caps omit runtime objects, input and native sorting scratch/comparisons, so they are not byte, time or word-RAM bounds. The duplicate-value control has two valid selections; repeated IDs are refused.
150 live solver controls cover 1,080 tiny target queries and ten generated cases. Existing CP-SAT already proposes exactly checked selections for repeated64 and distinct-powers32. A directly checked positive witness can suffice when count/reference search is unknown. Satisfaction OPTIMAL is no uniqueness/count certificate; solver INFEASIBLE remains a solver report unless independent negative evidence exists. Larger Python-exact totals are refused by the conservative integer adapter without rounding. Saved comparison.
/tmp/openai-math-scheduling-20261009-FKmLBr/bin/python3 research/tools/solve_and_audit_subset_sum.py research/fixtures/subset-sum-duplicate-identities-2026-10-09-v1.json
The preserved isolated OR-Tools 9.15.6755 environment was reused without installation changes. These are single-run generated controls, not real accounting data or speed comparisons. Updated dossier.
The source-parameter plans expose known 64-bit main guards at 600,000 and 36 billion items, with further fixed cutoffs unevaluated. At n64 and conditional all-call error budget 1/1,000,000, 261 odd-majority repetitions are assigned per two-sided adaptive decision query. This requires fresh independent genuine base-error calls, not implemented source programs. A verified positive witness and probabilistic NO remain distinct. Fast time and companion low-space claims cannot be combined.
Current documentary evidence
The eighteen-contract registry keeps the two subset-sum paper-level models separate. Fourteen controls test linter/registry behavior. Two self-authored product claims each have 18 documentary gaps. The current joined report archives six exact inputs, alongside 2,933 pinned source hashes. Synthetic completeness verifies no evidence, proof or applicability.
Earlier bundle editions and the frozen ten-case expert packet retain their historical tools/contracts. Expert comparison, source kernel/program acceptance, unrestricted performance and recurring buyer value remain pending. Feasibility, pilot.