After the opening 16 and the reply 26, naming 88 reaches U. U is a P-position, so 88 answers 26 and the reply 26 to the opening 16 loses. U is short, so by the Quiet End Theorem it is P exactly when each of its 59 obligations, the moves listed below, leads to an N-position. Every one of them is covered; the last, move 82, reaches X, which is N.
What it rests on. Most obligations are Book certificates; move 70's witness is too large for The Book and has native and Python replays; moves 8, 12, 36 and 56 go through repository certificates of infinite P-positions (G, F and V), and move 98 reaches Q, answered by 62 into W, which is P. Like W's, these certificates assume three published P-positions ({8,10,12,14} and {8,12,26,30} from Blok's pairing family, and Sicherman's {8,10,22}); the result lists everything.
X. X = {16,26,82,88} is N: its reply 701 reaches {16,26,82,88,701}, a P-position with Frobenius number 819. That is a finite computation of about 634 million states. Two engines with independent move code replayed it sequentially, in place of native and Python replays, which would not fit the host. They agree on the exact state count, and each certifies its whole memo. Every smaller odd reply is N (X's record).
Loading the audit from the repository…
| Move | Position | Evidence | Answer | States | Check |
|---|
Source: the campaign result
and its audit.json, produced by python sylver/campaigns/u-2026-09-27/audit.py.
Back to W, The Book, or the
solver demo.