files / problems / projective-plane-order-twelve / compute / README.md

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Compute — projective plane of order 12

Replay:

python3 replay_identities.py
python3 classify_types.py
python3 macneish_pair.py certs/macneish_involution_2mols.json
python3 verify_involution_mols.py --json certs/macneish_involution_2mols.json
python3 verify_involution_mols.py --json certs/t2_squares.json
./drat-trim certs/mate_t2.cnf certs/mate_t2.drat
./drat-trim certs/mate_macneish.cnf certs/mate_macneish.drat

The last two CNFs are regenerated by encode_mate.py from the family JSON; the checked DRAT files match the CNFs written tonight.

artifact claim
certs/identities.json v=157v=157, pair count, ∣det⁡B∣=13⋅1278\lvert\det B\rvert=13\cdot12^{78}, Bruck–Ryser silent
certs/type_classification.json remaining Aut-element types after divisibility
certs/macneish_involution_2mols.json explicit involution 2-MOLS (MacNeish product)
certs/t1_squares.json, certs/t2_squares.json SAT witnesses for t=1,2t=1,2
certs/mate_t2.drat, certs/mate_macneish.drat verified UNSAT: those two 2-families have no third involution-mate
certs/t3b.cnf / certs/t3c.out t=3t=3 cell-symbol; kissat UNKNOWN at 2396s / 45M conflicts
certs/sd3.cnf / certs/sd3.out t=3t=3 σ,δ\sigma,\delta; kissat UNKNOWN at 2396s / 21M conflicts

kissat 4.0.4 and drat-trim are local copies. Do not treat a SAT timeout as an exclusion.