{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:DDM4OAZVS7AMWZHRBI3HRKC5TO","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"95cab35ebf2d3193936200c4f79245695617d33dea27ec1a2a52bfc562fdf347","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2023-10-06T12:56:58Z","title_canon_sha256":"d530aa5c252d0ab5dba8959481bcf5741acecb92ff6a7b4ead0e9fac96d731cc"},"schema_version":"1.0","source":{"id":"2310.04211","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2310.04211","created_at":"2026-07-05T10:13:26Z"},{"alias_kind":"arxiv_version","alias_value":"2310.04211v2","created_at":"2026-07-05T10:13:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2310.04211","created_at":"2026-07-05T10:13:26Z"},{"alias_kind":"pith_short_12","alias_value":"DDM4OAZVS7AM","created_at":"2026-07-05T10:13:26Z"},{"alias_kind":"pith_short_16","alias_value":"DDM4OAZVS7AMWZHR","created_at":"2026-07-05T10:13:26Z"},{"alias_kind":"pith_short_8","alias_value":"DDM4OAZV","created_at":"2026-07-05T10:13:26Z"}],"graph_snapshots":[{"event_id":"sha256:5c73b3b5cd04e2a809fd763a12ceccb00507f6056154d8072468af132cb0608d","target":"graph","created_at":"2026-07-05T10:13:26Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2310.04211/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"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 $\\phi:\\mathcal{C}\\rightarrow \\mathcal{C}'$. 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","authors_text":"Chandrika Sadanand, Emily Shinkle","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2023-10-06T12:56:58Z","title":"Flip graph and arc complex finite rigidity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2310.04211","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:ee768e9f59718181545f74ea78bb78047f156736379895633a3e11bb6ab677fa","target":"record","created_at":"2026-07-05T10:13:26Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"95cab35ebf2d3193936200c4f79245695617d33dea27ec1a2a52bfc562fdf347","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2023-10-06T12:56:58Z","title_canon_sha256":"d530aa5c252d0ab5dba8959481bcf5741acecb92ff6a7b4ead0e9fac96d731cc"},"schema_version":"1.0","source":{"id":"2310.04211","kind":"arxiv","version":2}},"canonical_sha256":"18d9c7033597c0cb64f10a3678a85d9baaccc64f9e9744b9f3fb7bc535fd69af","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"18d9c7033597c0cb64f10a3678a85d9baaccc64f9e9744b9f3fb7bc535fd69af","first_computed_at":"2026-07-05T10:13:26.049857Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T10:13:26.049857Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"pIe7YEEo2u99JydS9d2SG0cNC5niV31CXsNwfOp0nvSZA3FD4f0siuc4VynMK5fe/R9WemPVF6SjmEXJqrr4DQ==","signature_status":"signed_v1","signed_at":"2026-07-05T10:13:26.050338Z","signed_message":"canonical_sha256_bytes"},"source_id":"2310.04211","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ee768e9f59718181545f74ea78bb78047f156736379895633a3e11bb6ab677fa","sha256:5c73b3b5cd04e2a809fd763a12ceccb00507f6056154d8072468af132cb0608d"],"state_sha256":"8203d76aa02fab6b6a54d20279c7fe570e8356ac236adc0dc1822a950fa5418f"}