Capture-Quiet Decomposition: A Verification Theorem for Chess Endgame Tablebases
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908949284913152 |
|---|---|
| author | Pavlov, Alexander |
| author_facet | Pavlov, Alexander |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07907 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Capture-Quiet Decomposition: A Verification Theorem for Chess Endgame Tablebases Pavlov, Alexander Artificial Intelligence Logic in Computer Science 68T20 I.2.1 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. |
| title | Capture-Quiet Decomposition: A Verification Theorem for Chess Endgame Tablebases |
| topic | Artificial Intelligence Logic in Computer Science 68T20 I.2.1 |
| url | https://arxiv.org/abs/2604.07907 |