In Sylver Coinage, W is the position after the numbers 16, 26, 62 and 98 have been named. Every number W generates is even, so infinitely many moves remain; but W is short, so by the Quiet End Theorem it is a P-position (the player to move loses) exactly when each of its 52 obligations, the moves listed below, leads to an N-position. Each one does. For moves 12 and 36 the evidence goes through repository certificates that 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 the claim rests on.
Consequences. Q = {16,26,88,98} is N, because naming 62 from Q reaches W. Together with X = {16,26,82,88} being N (October 6), that makes U = {16,26,88} P: 88 answers 26, and the reply 26 to the opening 16 loses. The opening 16 remains open.
Check it yourself. Book certificates with small finite leaves can
be replayed here by the independent JavaScript checker and in-browser
solver of The Book; the others are replayed by
python -m sylver.arena book verify. Two moves rest on
repository certificates of infinite P-positions, named in their rows. The
same audit style shows that U is P.
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/w-p-2026-09-27/audit.py,
which recomputes W's obligations with the arena referee's profile. Back to
The Book, the solver demo, or the
campaign tables.