{"paper":{"title":"On the number of fixed points of sofic flip systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Sieye Ryu, Young-One Kim","submitted_at":"2011-12-20T14:37:54Z","abstract_excerpt":"In the case when $X$ is a sofic shift and $\\phi : X \\to X$ is a homeomorphism such that $\\phi^2 = \\text{id}_X$ and $\\phi \\sigma_X = \\sigma_X^{-1} \\phi$, the number of points in $X$ that are fixed by $\\sigma_X^m$ and $\\sigma_X^n \\phi$, $m=1,2,...$, $n\\in\\Bbb Z$, is expressed in terms of a finite number of square matrices: The matrices are obtained from Krieger's joint state chain of a sofic shift which is conjugate to $X$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.4706","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"}