{"paper":{"title":"Minimal unknotting sequences of Reidemeister moves containing unmatched RII moves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Chuichiro Hayashi, Minori Sawada, Miwa Hayashi, Sayaka Yamada","submitted_at":"2010-11-17T14:07:12Z","abstract_excerpt":"Arnold introduced invariants $J^+$, $J^-$ and $St$ for generic planar curves.\n  It is known that both $J^+ /2 + St$ and $J^- /2 + St$ are invariants for generic spherical curves.\n  Applying these invariants to underlying curves of knot diagrams, we can obtain lower bounds for the number of Reidemeister moves for uknotting.\n  $J^- /2 + St$ works well for unmatched RII moves.\n  However, it works only by halves for RI moves.\n  Let $w$ denote the writhe for a knot diagram.\n  We show that $J^- /2 + St \\pm w/2$ works well also for RI moves, and demonstrate that it gives a precise estimation for a ce"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.3963","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"}