After the opening 16 and the reply 30, naming 56 reaches Z. Z is short, so by the Quiet End Theorem it is P exactly when each of its 52 obligations, the moves listed below, leads to an N-position. Every one is covered, so the reply 30 to the opening 16 loses. With the certified answers for 2–24, U for 26, Y for 28, and Hutchings' theorem for the odd replies, every reply to 16 up to 30 now has an answer.
What it rests on. Move 44 is answered by 40 into a second short P-position, Z′ = {16,30,40,44}, whose 40 obligations the same audit covers. Z′ is on Sicherman's list of P-positions; this confirms it independently. Most obligations have finite witnesses replayed natively and in Python; the two largest (70→311 and 130→225, about 300 and 260 million states) have native and sequential Kunz replays, since the Python evaluator does not fit this host. The certified nodes C, E, F, O and K bring in Blok's pairing family and, through O and K, Sicherman's {8,10,22}. The result lists everything.
Loading the audit from the repository…
| Move | Position | Evidence | Answer | States | Check |
|---|
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/z-2026-10-08/audit.py.
Back to Y, U, W, The Book, or the
solver demo.