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We say that a cell complex exhibits \\emph{finite rigidity} if it contains a finite rigid subcomplex. Given a surface with marked points, its \\textit{flip graph} and \\textit{arc complex} are simplicial complexes indexing the triangulations and the arcs between marked points, respectively"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"2310.04211","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2023-10-06T12:56:58Z","cross_cats_sorted":[],"title_canon_sha256":"d530aa5c252d0ab5dba8959481bcf5741acecb92ff6a7b4ead0e9fac96d731cc","abstract_canon_sha256":"95cab35ebf2d3193936200c4f79245695617d33dea27ec1a2a52bfc562fdf347"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:13:26.050338Z","signature_b64":"pIe7YEEo2u99JydS9d2SG0cNC5niV31CXsNwfOp0nvSZA3FD4f0siuc4VynMK5fe/R9WemPVF6SjmEXJqrr4DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"18d9c7033597c0cb64f10a3678a85d9baaccc64f9e9744b9f3fb7bc535fd69af","last_reissued_at":"2026-07-05T10:13:26.049857Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:13:26.049857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Flip graph and arc complex finite rigidity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Chandrika Sadanand, Emily Shinkle","submitted_at":"2023-10-06T12:56:58Z","abstract_excerpt":"A subcomplex $\\mathcal{X}$ of a cell complex $\\mathcal{C}$ is called \\emph{rigid} with respect to another cell complex $\\mathcal{C}'$ if every injective simplicial map $\\lambda:\\mathcal{X} \\rightarrow \\mathcal{C}'$ has a unique extension to an injective simplicial map $\\phi:\\mathcal{C}\\rightarrow \\mathcal{C}'$. 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