Reply 38 after 16: four P-positions refute five answers

After the opening 16, the lowest reply with no certified answer is 38. {16,38} is short, so by the Quiet End Theorem a move answers 38 only if it is one of its 98 obligations. This record certifies four short P-positions, I = {16,20,22,24}, B28 = {16,28,38,40}, B24 = {16,24,38,44} and B56 = {16,38,56,60}. I and B24 are on Sicherman's list of P-positions, so for them this is an independent confirmation; B28 and B56 are not on it. Each is P because every one of its obligations, listed below, leads to an N-position. They show that 24, 28, 40, 44 and 56 do not answer 38; with the certified nodes C, E, F and P0, the audit also rules out 4, 6, 8, 12, 14 and 22. The result records the search, which found on October 18, by search and not yet certified, that {16,38,72} is P, so 72 answers 38.

What it rests on. Finite witnesses are replayed natively and in Python; B56's four largest (180 to 424 million states) natively and by a sequential Kunz run instead. The certified nodes C, D, E, F, J and P0 bring in Blok's pairing family, as in Y; nothing here rests on Sicherman's {8,10,22}.

The answers to 38 the audit refutes

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B56 = {16,38,56,60}

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B24 = {16,24,38,44}

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B28 = {16,28,38,40}

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I = {16,20,22,24}, which answers B24's move 20

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Source: the campaign result and its audit.json, produced by python sylver/campaigns/r38-2026-10-09/audit.py. Back to Z, Y, U, The Book, or the solver demo.