{"paper":{"title":"Unique Winning Opening Move in Three-Row Chomp","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Erez Sheiner","submitted_at":"2026-05-22T16:45:26Z","abstract_excerpt":"Chomp was introduced by Gale in 1974. In the same paper, Gale reported that the 3 x n games had been completely analyzed for n <= 100, with a unique winning first move in every case, and asked whether winning first moves are unique in general. Although the general uniqueness statement is false, we prove that the three-row uniqueness phenomenon suggested by Gale's computations holds for all n: every 3 x n Chomp rectangle has exactly one winning opening move. This settles the three-row case of Gale's 52-year-old first-move uniqueness question.\n  The proof is carried out in the two-variable recur"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.23837","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.23837/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}