{"paper":{"title":"Progress on mis\\`ere dead ends: game comparison, canonical form, and conjugate inverses","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carlos Santos, Gabriel Renault, Rebecca Milley, Richard Nowakowski, Urban Larsson","submitted_at":"2018-07-30T11:48:43Z","abstract_excerpt":"This paper addresses several significant gaps in the theory of restricted mis\\`ere play (Plambeck, Siegel 2008), primarily in the well-studied universe of dead-ending games, $\\mathcal{E}$ (Milley, Renault 2013); if a player run out of moves in $X\\in \\mathcal E$, then they can never move again in any follower of $X$. A universe of games is a class of games which is closed under disjunctive sum, taking options and conjugates. We use novel results from absolute combinatorial game theory (Larsson, Nowakowski, Santos 2017) to show that $\\mathcal{E}$ and the universe $\\mathcal{D}\\subset \\mathcal{E}$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.11297","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":""},"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"}