Capture-Quiet Decomposition: A Verification Theorem for Chess Endgame Tablebases

• URL: http://arxiv.org/abs/2604.07907v1
• Date: Thu, 09 Apr 2026 07:22:24 GMT
• Title: Capture-Quiet Decomposition: A Verification Theorem for Chess Endgame Tablebases
• Abstract summary: We present the Capture-Quiet Decomposition (CQD) for verifying Win-Draw-Loss labelings of chess endgame tablebases.<n>The theorem decomposes every legal position into exactly one of three categories -- terminal, capture, or quiet.<n>We validate CQD exhaustively on all 35 three- and four-piece endgames (42 million positions), all 110 five-piece endgames, and all 372 six-piece endgames -- 517 endgames in total.
• Score: 51.56484100374058
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: We present the Capture-Quiet Decomposition (CQD), a structural theorem for verifying Win-Draw-Loss (WDL) labelings of chess endgame tablebases. The theorem decomposes every legal position into exactly one of three categories -- terminal, capture, or quiet -- and shows that a WDL labeling is correct if and only if: (1) terminal positions are labeled correctly, (2) capture positions are consistent with verified sub-models of smaller piece count, and (3) quiet positions satisfy retrograde consistency within the same endgame. The key insight is that capture positions anchor the labeling to externally verified sub-models, breaking the circularity that allows trivial fixpoints (such as the all-draw labeling) to satisfy self-consistency alone. We validate CQD exhaustively on all 35 three- and four-piece endgames (42 million positions), all 110 five-piece endgames, and all 372 six-piece endgames -- 517 endgames in total -- with the decomposed verifier producing identical violation counts to a full retrograde baseline in every case.

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