Twelve runnable research utilities

The ten earlier utilities now have two additional components for the data and allocation candidates. All are local research prototypes with separate evidence limits; none demonstrates buyer demand, profitability or independent validity of the source proofs.

New fixed-margin reference

contingency_reference.py uses conventional row dynamic programming to count small fixed-margin integer tables and map ranks to tables. It supports explicit cell bounds and structural zeros. A uniformly selected rank maps to a uniform table; optional draws use secrets.randbelow and record ranks for replay. This law differs from fixed-margin conditional independence.

The reference is limited to at most six rows/columns, total 128, 50,000 memo states and a count-work budget of one million units. Work units count newly evaluated memo states and visited row-prefix nodes; they are not measured bit operations or a wall-time guarantee. A separate sampling budget caps output work. Counting exhaustion returns unknown with exact_count=null; completed infeasibility returns zero. Count-complete sampling exhaustion preserves the count and any completed tables. It does not implement the source's unrestricted polynomial-bit sampler or FPRAS, and provides no privacy guarantee.

python3 research/tools/contingency_reference.py research/fixtures/contingency-two-by-two.json --rank 0 --rank 1 --rank 2
python3 research/tools/contingency_reference.py research/fixtures/contingency-two-by-two.json --random-samples 4

325 saved checks cover closed-form two-by-two counts, rank coverage, independent Cartesian fixtures, structural zeros, permutation counts, invalid input and budget semantics. The exact law comparison gives distance 1/3 from the conditional-independence law in the two-by-two example. Saved deterministic example.

New matching certificate audit

audit_matching_certificate.py checks a matching's edges and endpoint disjointness on a simple unweighted graph. It removes a supplied vertex subset S, counts odd components, and checks the upper bound (n-q+|S|)/2 together with floor(n/2). A feasible candidate attaining a bound is certified maximum cardinality. A loose bound leaves optimality unknown; invalid candidates receive no certificate. It hashes the input record and records the exact objective.

The input cap is 100,000 vertices and 500,000 edges. The connected-component pass is linear in graph size; the audit also validates and hashes the input. It does not construct a matching or the subset, implement the new source backend, handle weighted objectives or establish model fairness. Its program has not been formally verified.

python3 research/tools/audit_matching_certificate.py research/fixtures/star-matching-certificate.json

1,042 saved checks include all 1,024 five-vertex graphs and 32,768 subset bounds against a separate brute-force matching optimizer. Additional cases distinguish invalid, maximum and inconclusive candidates. Saved star certificate. This is finite component validation, not a source-algorithm speed benchmark or proof for an arbitrary implementation.

Full current utility list

The eight component validation reports now record 1,473 passed checks. Most of the added checks are exhaustive small-graph and small-table cases. Earlier static, withdrawal and embedding fixtures are separate evidence; none is a mathematical kernel check or a buyer-value test.

All saved-output commands require fresh filenames or directories and preserve earlier editions. The dated batch/validation drivers should not be rerun into existing paths. Explicit direct-backend parameter calculations explain why the new finite utilities are separate from the deferred literal research algorithms.