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
| statement | cell | tag | queries | UNSAT | SAT | DRAT verified | proof kept | proof size, MB |
|---|---|---|---|---|---|---|---|---|
| R | (4,4,4) | 16 | 16 | 0 | 16 | 16 | 1.2 | |
| R | (5,5,5) | 20 | 20 | 0 | 20 | 20 | 12.4 | |
| R | (6,6,6) | 24 | 24 | 0 | 24 | 24 | 102.0 | |
| S | (4,4,4) | 4 | 4 | 0 | 4 | 4 | 0.3 | |
| S | (5,5,5) | 6 | 6 | 0 | 6 | 6 | 3.6 | |
| S | (6,6,6) | 8 | 8 | 0 | 8 | 8 | 28.0 | |
| U | (4,4,4) | 16 | 16 | 0 | 16 | 4 | 619.1 | |
| U | (5,5,5) | 16 | 16 | 0 | 16 | 0 | 2,101.3 | |
| U | (6,6,6) | 4 | 4 | 0 | 4 | 0 | 1,395.2 | |
| total | 114 | 114 | 0 | 114 | 82 | 4,262.9 | ||
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
| statement | cell | tag | queries | UNSAT | SAT | DRAT verified | proof kept | proof size, MB |
|---|---|---|---|---|---|---|---|---|
| U | (3,3,12) | F2 | 48 | 48 | 0 | 0 | 0 | 0.0 |
| U | (3,3,12) | F3 | 48 | 48 | 0 | 48 | 48 | 1,603.1 |
| U | (3,3,12) | preflight | 1 | 1 | 0 | 0 | 0 | 0.0 |
| U | (3,3,9) | F2 | 48 | 48 | 0 | 0 | 0 | 0.0 |
| U | (3,3,9) | F3 | 48 | 48 | 0 | 48 | 48 | 1,197.6 |
| U | (3,3,9) | mainloop-recheck | 16 | 16 | 0 | 0 | 0 | 0.0 |
| U | (3,3,9) | preflight | 2 | 2 | 0 | 0 | 0 | 0.0 |
| U | (4,4,8) | F2 | 48 | 48 | 0 | 0 | 0 | 0.0 |
| U | (4,4,8) | F3 | 48 | 48 | 0 | 48 | 0 | 5,306.1 |
| U | (4,4,8) | preflight | 2 | 2 | 0 | 0 | 0 | 0.0 |
| U | (6,6,6) | preflight | 1 | 1 | 0 | 0 | 0 | 0.0 |
| U | (6,6,9) | F2 | 48 | 48 | 0 | 0 | 0 | 0.0 |
| U | (6,6,9) | F3 | 3 | 3 | 0 | 3 | 0 | 2,406.4 |
| U | (6,6,9) | preflight | 1 | 1 | 0 | 0 | 0 | 0.0 |
| U | (7,7,7) | F2 | 16 | 16 | 0 | 0 | 0 | 0.0 |
| U | (7,7,7) | F3 | 4 | 4 | 0 | 4 | 0 | 4,047.1 |
| U | (7,7,7) | mainloop-recheck | 1 | 1 | 0 | 1 | 0 | 864.1 |
| U | (7,7,7) | preflight | 1 | 1 | 0 | 0 | 0 | 0.0 |
| U | (8,8,8) | F2 | 16 | 16 | 0 | 0 | 0 | 0.0 |
| U | (8,8,8) | F3 | 4 | 4 | 0 | 4 | 0 | 9,348.8 |
| U | (8,8,8) | preflight | 1 | 1 | 0 | 0 | 0 | 0.0 |
| total | 405 | 405 | 0 | 156 | 96 | 24,773.2 | ||