Certificate ledgers

The machine-checked evidence for the certified claims. Each line of a ledger records one SAT query: the statement and cell it encodes, the SHA-256 of the CNF formula, the solver's verdict, and, where a proof was produced, the size and SHA-256 of the DRAT proof and the verdict of the independent checker drat-trim. A query with verdict UNSAT and a DRAT proof verified by drat-trim is a machine-checked proof that no state of the kind encoded exists on that cell. Queries without a proof (for instance pre-flight runs) are solver verdicts only. The formulas and proofs themselves (hundreds of megabytes to gigabytes) are not published; they are regenerated by the scripts named on the claim pages and checked against the hashes in the *_sha256_*.txt files. The statement letters and tags are those of the ledgers; the claim pages and the campaign reports explain them.

Counts below are computed from the ledgers when the site is built.

h28x_results.jsonl

raw ledger (JSON lines) · h28x_sha256_2026-09-27.txt
sha256 of the ledger 10c40341ed35df8b4934c5c9b99fe8cda089ede59bd03bc031d9ff8579d4e2e5
Cited by: theorem-h-orientation/ku, theorem-h-orientation/u-prime-certificates-2026-09-27

statementcelltagqueriesUNSATSATDRAT verifiedproof keptproof size, MB
R(4,4,4)1616016161.2
R(5,5,5)20200202012.4
R(6,6,6)242402424102.0
S(4,4,4)440440.3
S(5,5,5)660663.6
S(6,6,6)8808828.0
U(4,4,4)16160164619.1
U(5,5,5)161601602,101.3
U(6,6,6)440401,395.2
total1141140114824,262.9

h74x_results.jsonl

raw ledger (JSON lines) · h74x_sha256_2026-10-01.txt
sha256 of the ledger 598aa9d34477c33f864a09d1792d12551a86039c1e72a48b18544f89fb1f8346
Cited by: theorem-h-orientation/u-prime-certificates-2026-10-01

statementcelltagqueriesUNSATSATDRAT verifiedproof keptproof size, MB
U(3,3,12)F248480000.0
U(3,3,12)F34848048481,603.1
U(3,3,12)preflight110000.0
U(3,3,9)F248480000.0
U(3,3,9)F34848048481,197.6
U(3,3,9)mainloop-recheck16160000.0
U(3,3,9)preflight220000.0
U(4,4,8)F248480000.0
U(4,4,8)F3484804805,306.1
U(4,4,8)preflight220000.0
U(6,6,6)preflight110000.0
U(6,6,9)F248480000.0
U(6,6,9)F3330302,406.4
U(6,6,9)preflight110000.0
U(7,7,7)F216160000.0
U(7,7,7)F3440404,047.1
U(7,7,7)mainloop-recheck11010864.1
U(7,7,7)preflight110000.0
U(8,8,8)F216160000.0
U(8,8,8)F3440409,348.8
U(8,8,8)preflight110000.0
total40540501569624,773.2