{"paper":{"title":"Bounding Game Temperature Using Confusion Intervals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Carlos Pereira dos Santos, Richard J. Nowakowski, Svenja Huntemann","submitted_at":"2019-08-22T16:05:30Z","abstract_excerpt":"For combinatorial games, temperature is a measure of the volatility, that is, by how much the advantage can change. Typically, the temperature has been measured for individual positions within specific games. In this paper, we give the first general upper bounds on the temperature for any class of games.\n  For a position $G$, the closure of the set of numbers $\\{g\\}$ such that $G-g$ is a first player win, is called the confusion interval of $G$. Let $\\ell(G)$ be the length of this interval. Our first main result is: For a class of games $\\mathscr{S}$, if there are constants $J$ and $K$ such th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.08471","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/1908.08471/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"}