Thirty-four runnable research utilities

Forty-nine saved component reports contain 19,891 passed checks. The new exact-library and selected source-guard comparison adds 2,023 controls to the preceding 17,868. It is supporting research tooling, so the utility count remains 34. Source proof/program acceptance, buyer value and profitable delivery remain unverified.

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	Twenty-one 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
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	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	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	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

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.

Literal packaging and source-derived count stage

1,445 controls compare 469 tiny collections with every binary output word through length nine. Exact overlap DP matches their unrestricted optimum within this finite alphabet/domain. Paper forced counts do not exceed actual occurrences in every common word in that domain. Artifact round trips, original IDs, empty/duplicate/zero/UTF8 byte values, invalid models and budgets are checked.

python3 research/tools/superstring_packaging_reference.py research/prototypes/literal-packing-comparison-2026-10-09-v1/synthetic_greedy_gap-input.json
python3 research/tools/superstring_counts_reference.py research/prototypes/literal-packing-comparison-2026-10-09-v1/synthetic_periodic_windows-input.json

Seven saved comparisons and 31 emitted .ssp files include stable IDs/header/offset-length data. The public 48-title sample shrinks raw SSP1 by 28 bytes, leaves gzip unchanged at 1,685 and increases XZ from 1,616 to 1,648. A synthetic periodic sample shrinks SSP1 from 308 to 228 and gzip from 163 to 138, already with ordinary greedy. The generated greedy-gap control takes 10 raw bytes versus exact 9. Complete artifact objectives and API constraints matter; no customer, linker or access-performance result is inferred.

The count-stage reference implements source section02 only. For a^16 it recovers W=16 and m(a^k)=17-k. Source W validity in general depends on its unverified proof; finite comparisons do not certify that proof. The full forced-count/periodic-layer/request/link/cycle/Euler factor-two construction is unimplemented. The package model uses immutable length-aware bytes, not drop-in C strings or preserved pointer identity. Revised dossier.

Exact polynomial and numerical-range evidence

857 controls include 625 independent complex Hermitian 2-by-2 PSD oracle cases, zero pivots, exact rounding, eight generated matrices/polynomials, tensor order, finite Rayleigh probes, thresholds and budgets. An exact complete Gram PSD check supplies finite norm-threshold evidence independently of Crouzeix. Formal Python correctness was not proved.

python3 research/tools/numerical_range_polynomial_reference.py research/prototypes/numerical-range-comparison-2026-10-09-v1/nilpotent_sharp-input.json --grid 32

The separate twenty-direction PSD support enclosure and covered-cell Lipschitz/Frobenius calculation gives an entire-domain upper. The source constant-two result is conditional; the prior published constant is rounded upward to 483/200. On the sharp nilpotent example, the source-conditional upper about 2.189 fits tolerance 2.2 while the prior upper about 2.644 does not. A direct exact norm-two check already suffices with 231 charges, versus 84,404 for the full reference. No standalone library advantage is established. Eight-case report.

195 SciPy diagnostic controls reuse the existing isolated SciPy 1.18.1/NumPy 2.5.3 environment without installation changes. SVD/eigvalsh agreement is finite and tolerance bounded, not a rigorous library rounding guarantee. Revised numerical dossier.

Facility-planning evidence

5,127 controls include 4,992 models over all 52 three-point integer metrics with distances 1-4, compared with a separate all-subsets oracle. Rational primal/dual checks, false witnesses, full-metric conditions, model rejection, overlap and unknown budget states are included. The exact reference is conventional and exponential, not the source approximation algorithm.

python3 research/tools/metric_facility_reference.py research/prototypes/metric-facility-comparison-2026-10-09-v1/dual_tight_line-input.json --dual research/prototypes/metric-facility-comparison-2026-10-09-v1/dual_tight_line-dual.json --subset-budget 0

34 existing-solver controls compare eight generated cases with the preserved OR-Tools 9.15.6755 runtime. Seven OPTIMAL results match independent tiny optima. The 24-location/12-site case returns FEASIBLE with cost 12; a separate exact dual also gives 12 and proves optimality without enumeration. Four added controls, inputs and comparison.

Caps are 48 locations,128-bit canonical rational inputs, 100,000 enumerated subsets and five million enumeration distance lookups. Parsing/metric checks, primal/dual checks, rational bit arithmetic, allocations and time are outside those counters. Budget exhaustion preserves only completed evidence. Weights, capacities, directed distances and other real constraints need separate models. First product experiment.

Current documentary evidence

The twenty-one-contract registry now has 76 exact source-file pointers. The new metric-facility contract distinguishes fixed accuracy, strict rational metrics, unweighted demand, candidate budget, full source implementation, recovery promises and instance-specific bounds. Seven documentary controls passed. The new joined report has 16 gaps in a self-authored claim, 2,933 source hashes and six archived exact inputs; documentation completeness accepts no evidence contents.

Historical bundles and the frozen ten-case expert packet remain preserved. Source proof acceptance, actual reviewer comparison and paid customer value remain open. Feasibility, pilot.

Edit-distance source activation and existing exact tools

The selected source's large branch requires ell >= 2^1000. Its first necessary guard activates only at symbolic length 2^(2^(2^999))-1; full physical eligibility has additional accuracy and bit-width requirements. At N=10^12, ell=8. This makes the literal backend unsuitable for a practical first product. The source estimate is probabilistic on both sides and supplies no edit script.

A fresh isolated RapidFuzz 3.14.6 comparison adds 2,023 finite/library/guard controls. Exact routines already supply distances, cutoff predicates and alignments. On a generated 65,536-symbol shifted pair, unrestricted distance took about 101 ms median; a cutoff query took about 0.13 ms. These different output requirements and synthetic timings supply no source-backend speedup or customer benefit. A cutoff sentinel and normalization changes must be represented correctly. Detailed report, revised dossier.

Keep direct edit-distance commercialization deferred and conventional integration confidence low. The facility-planning review workflow remains the first product experiment; its buyer demand is still unvalidated.