{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:24M75OO3O276AHDJGMSXKLU467","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":"ef1fbd8dda2274338baada26fad6cb6da128795beaf7153105c74f3683f19d4b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-10-13T14:18:57Z","title_canon_sha256":"ada4d7635ecb2d0e88a4982749fc24228579c5870822bcf50c99170a5b300210"},"schema_version":"1.0","source":{"id":"1410.3321","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1410.3321","created_at":"2026-05-18T00:28:57Z"},{"alias_kind":"arxiv_version","alias_value":"1410.3321v2","created_at":"2026-05-18T00:28:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.3321","created_at":"2026-05-18T00:28:57Z"},{"alias_kind":"pith_short_12","alias_value":"24M75OO3O276","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_16","alias_value":"24M75OO3O276AHDJ","created_at":"2026-05-18T12:28:09Z"},{"alias_kind":"pith_short_8","alias_value":"24M75OO3","created_at":"2026-05-18T12:28:09Z"}],"graph_snapshots":[{"event_id":"sha256:f2f51430f714fb39de4190c7167f74ee76813a4c2c81edb7e20857e93b0e4298","target":"graph","created_at":"2026-05-18T00:28:57Z","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":"Simple crystallizations are edge-coloured graphs representing PL 4-manifolds with the property that the 1-skeleton of the associated triangulation equals the 1-skeleton of a 4-simplex. In the present paper, we prove that any (simply-connected) PL $4$-manifold $M$ admitting a simple crystallization admits a special handlebody decomposition, too; equivalently, $M$ may be represented by a framed link yielding $\\mathbb S^3$, with exactly $\\beta_2(M)$ components ($\\beta_2(M)$ being the second Betti number of $M$). As a consequence, the regular genus of $M$ is proved to be the double of $\\beta_2(M)$","authors_text":"C. Gagliardi, M.R. Casali, P. Cristofori","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-10-13T14:18:57Z","title":"PL 4-manifolds admitting simple crystallizations: framed links and regular genus"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3321","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:a9732551c0e161c2e8931b53ef9970da49e8e24d9238310bd53ae6acf7f9852f","target":"record","created_at":"2026-05-18T00:28:57Z","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":"ef1fbd8dda2274338baada26fad6cb6da128795beaf7153105c74f3683f19d4b","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-10-13T14:18:57Z","title_canon_sha256":"ada4d7635ecb2d0e88a4982749fc24228579c5870822bcf50c99170a5b300210"},"schema_version":"1.0","source":{"id":"1410.3321","kind":"arxiv","version":2}},"canonical_sha256":"d719feb9db76bfe01c693325752e9cf7dad31377b21159b85260d56264843808","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d719feb9db76bfe01c693325752e9cf7dad31377b21159b85260d56264843808","first_computed_at":"2026-05-18T00:28:57.337022Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:28:57.337022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sp1Cw5PWe/25zs2XDeZFxatT6yK3b3aQ0L1RfRrm4/+Rdu3QYVsyEJUhrnTzUNd2hK81wquzph0YERYscc85DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:28:57.337602Z","signed_message":"canonical_sha256_bytes"},"source_id":"1410.3321","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a9732551c0e161c2e8931b53ef9970da49e8e24d9238310bd53ae6acf7f9852f","sha256:f2f51430f714fb39de4190c7167f74ee76813a4c2c81edb7e20857e93b0e4298"],"state_sha256":"c066f557bbff822b7c0b6edab4dba5a16901628586119f566ba67cdfbc221f50"}