{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:7UR4MTPLB3ONMA5N65ZZ4AMCC6","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":"d4a2ce17ec04fd2f01b11f93275b32e86e74ee7e9ab4a35473e9f8dde3714dcb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2008-04-04T11:52:32Z","title_canon_sha256":"246576189d68f21f66bb9bbb702d5f29bb980da5a036bc7e82b89a3beeb54ad6"},"schema_version":"1.0","source":{"id":"0804.0706","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0804.0706","created_at":"2026-05-17T23:55:23Z"},{"alias_kind":"arxiv_version","alias_value":"0804.0706v2","created_at":"2026-05-17T23:55:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0804.0706","created_at":"2026-05-17T23:55:23Z"},{"alias_kind":"pith_short_12","alias_value":"7UR4MTPLB3ON","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_16","alias_value":"7UR4MTPLB3ONMA5N","created_at":"2026-05-18T12:25:56Z"},{"alias_kind":"pith_short_8","alias_value":"7UR4MTPL","created_at":"2026-05-18T12:25:56Z"}],"graph_snapshots":[{"event_id":"sha256:bcc37cdff49777e67eeb9b040a39b818d4b97ee494aa3d052a337f60b4b2208a","target":"graph","created_at":"2026-05-17T23:55:23Z","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"},"paper":{"abstract_excerpt":"We prove that the classical set of moves for standard spines of 3-manifolds (i.e. the MP-move and the V-move) does not suffice to relate to each other any two standard skeleta of a 3-manifold with marked boundary. We also describe a condition on the 3-manifold with marked boundary that tells whether the generalised set of moves, made up of the MP-move and the L-move, suffices to relate to each other any two standard skeleta of the 3-manifold with marked boundary.\n  For the 3-manifolds with marked boundary that do not fulfil this condition, we give three other moves: the CR-move, the T1-move an","authors_text":"Gennaro Amendola","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2008-04-04T11:52:32Z","title":"Moves for standard skeleta of 3-manifolds with marked boundary"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0804.0706","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":"sha256:487b85da69b05c272bbea81e1cd9657dd27d7282411da9fdfb0da2d4943cc596","target":"record","created_at":"2026-05-17T23:55:23Z","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":"d4a2ce17ec04fd2f01b11f93275b32e86e74ee7e9ab4a35473e9f8dde3714dcb","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2008-04-04T11:52:32Z","title_canon_sha256":"246576189d68f21f66bb9bbb702d5f29bb980da5a036bc7e82b89a3beeb54ad6"},"schema_version":"1.0","source":{"id":"0804.0706","kind":"arxiv","version":2}},"canonical_sha256":"fd23c64deb0edcd603adf7739e018217a8c859d61c275a4fae3c90fb3a5df1c8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd23c64deb0edcd603adf7739e018217a8c859d61c275a4fae3c90fb3a5df1c8","first_computed_at":"2026-05-17T23:55:23.575512Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:55:23.575512Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9i1BowkH17LRTjskVjnWJT0OrMAr1hSU+pLe21RtapqrCEmMdUw1XMQkcVPBqS5t30vLgR0KBrZIAHSaFD7BAA==","signature_status":"signed_v1","signed_at":"2026-05-17T23:55:23.576044Z","signed_message":"canonical_sha256_bytes"},"source_id":"0804.0706","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:487b85da69b05c272bbea81e1cd9657dd27d7282411da9fdfb0da2d4943cc596","sha256:bcc37cdff49777e67eeb9b040a39b818d4b97ee494aa3d052a337f60b4b2208a"],"state_sha256":"deabca267154153797b3a357216fee26dbef908ab2a3aa423a2ef12dead98d2f"}