{"paper":{"title":"Reidemeister and movie moves for involutive links","license":"http://creativecommons.org/licenses/by/4.0/","headline":"A set of 39 equivariant movie moves connects any two movie presentations of equivariantly isotopic cobordisms between involutive links.","cross_cats":[],"primary_cat":"math.GT","authors_text":"Abhishek Mallick, Irving Dai, Maciej Borodzik, Matthew Stoffregen","submitted_at":"2026-04-29T07:30:08Z","abstract_excerpt":"An involutive link is a link which is invariant under the standard rotation by 180 degrees in $S^3$. We establish an equivariant analogue of the work of Carter and Saito aimed at studying equivariant cobordisms between involutive links. This gives a set of $39$ equivariant movie moves that suffice to go between any two movie presentations of a pair of equivariantly isotopic cobordisms. Along the way, we give a singularity-theoretic proof of the equivariant Reidemeister theorem and study loops of equivariant Reidemeister moves. Our approach proceeds by analyzing codimension $2$ singularities of"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"This gives a set of 39 equivariant movie moves that suffice to go between any two movie presentations of a pair of equivariantly isotopic cobordisms.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The classification of all codimension-2 singularities of equivariant maps from S^1 to R^2 is complete and that embedded equivariant Morse theory applies without extra obstructions not captured by the listed moves.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"39 equivariant movie moves generate all transitions between movie presentations of equivariantly isotopic cobordisms between involutive links, with a singularity-theoretic proof of the equivariant Reidemeister theorem.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A set of 39 equivariant movie moves connects any two movie presentations of equivariantly isotopic cobordisms between involutive links.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"b633cb3ab9d4795541c79ed736a21aaeb666d528c378748a4e527e0dd317043a"},"source":{"id":"2604.26369","kind":"arxiv","version":2},"verdict":{"id":"0820206e-245d-45b3-b38a-7f73ab0fc42c","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-07T12:33:00.008178Z","strongest_claim":"This gives a set of 39 equivariant movie moves that suffice to go between any two movie presentations of a pair of equivariantly isotopic cobordisms.","one_line_summary":"39 equivariant movie moves generate all transitions between movie presentations of equivariantly isotopic cobordisms between involutive links, with a singularity-theoretic proof of the equivariant Reidemeister theorem.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The classification of all codimension-2 singularities of equivariant maps from S^1 to R^2 is complete and that embedded equivariant Morse theory applies without extra obstructions not captured by the listed moves.","pith_extraction_headline":"A set of 39 equivariant movie moves connects any two movie presentations of equivariantly isotopic cobordisms between involutive links."},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2604.26369/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"ai_meta_artifact","ran_at":"2026-05-21T00:38:01.443423Z","status":"completed","version":"1.0.0","findings_count":0},{"name":"doi_compliance","ran_at":"2026-05-19T20:13:06.611557Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"e7dfb8ea951e075253603c9d7649f50c97c556c532581e408c7c84bc815f7e82"},"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"}