{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:24M75OO3O276AHDJGMSXKLU467","short_pith_number":"pith:24M75OO3","schema_version":"1.0","canonical_sha256":"d719feb9db76bfe01c693325752e9cf7dad31377b21159b85260d56264843808","source":{"kind":"arxiv","id":"1410.3321","version":2},"attestation_state":"computed","paper":{"title":"PL 4-manifolds admitting simple crystallizations: framed links and regular genus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"C. Gagliardi, M.R. Casali, P. Cristofori","submitted_at":"2014-10-13T14:18:57Z","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 $\\beta_2(M)$"},"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":"1410.3321","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.GT","submitted_at":"2014-10-13T14:18:57Z","cross_cats_sorted":[],"title_canon_sha256":"ada4d7635ecb2d0e88a4982749fc24228579c5870822bcf50c99170a5b300210","abstract_canon_sha256":"ef1fbd8dda2274338baada26fad6cb6da128795beaf7153105c74f3683f19d4b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:28:57.337602Z","signature_b64":"sp1Cw5PWe/25zs2XDeZFxatT6yK3b3aQ0L1RfRrm4/+Rdu3QYVsyEJUhrnTzUNd2hK81wquzph0YERYscc85DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d719feb9db76bfe01c693325752e9cf7dad31377b21159b85260d56264843808","last_reissued_at":"2026-05-18T00:28:57.337022Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:28:57.337022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"PL 4-manifolds admitting simple crystallizations: framed links and regular genus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"C. Gagliardi, M.R. Casali, P. Cristofori","submitted_at":"2014-10-13T14:18:57Z","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 $\\beta_2(M)$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3321","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1410.3321","created_at":"2026-05-18T00:28:57.337114+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.3321v2","created_at":"2026-05-18T00:28:57.337114+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.3321","created_at":"2026-05-18T00:28:57.337114+00:00"},{"alias_kind":"pith_short_12","alias_value":"24M75OO3O276","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"24M75OO3O276AHDJ","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"24M75OO3","created_at":"2026-05-18T12:28:09.283467+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/24M75OO3O276AHDJGMSXKLU467","json":"https://pith.science/pith/24M75OO3O276AHDJGMSXKLU467.json","graph_json":"https://pith.science/api/pith-number/24M75OO3O276AHDJGMSXKLU467/graph.json","events_json":"https://pith.science/api/pith-number/24M75OO3O276AHDJGMSXKLU467/events.json","paper":"https://pith.science/paper/24M75OO3"},"agent_actions":{"view_html":"https://pith.science/pith/24M75OO3O276AHDJGMSXKLU467","download_json":"https://pith.science/pith/24M75OO3O276AHDJGMSXKLU467.json","view_paper":"https://pith.science/paper/24M75OO3","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.3321&json=true","fetch_graph":"https://pith.science/api/pith-number/24M75OO3O276AHDJGMSXKLU467/graph.json","fetch_events":"https://pith.science/api/pith-number/24M75OO3O276AHDJGMSXKLU467/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/24M75OO3O276AHDJGMSXKLU467/action/timestamp_anchor","attest_storage":"https://pith.science/pith/24M75OO3O276AHDJGMSXKLU467/action/storage_attestation","attest_author":"https://pith.science/pith/24M75OO3O276AHDJGMSXKLU467/action/author_attestation","sign_citation":"https://pith.science/pith/24M75OO3O276AHDJGMSXKLU467/action/citation_signature","submit_replication":"https://pith.science/pith/24M75OO3O276AHDJGMSXKLU467/action/replication_record"}},"created_at":"2026-05-18T00:28:57.337114+00:00","updated_at":"2026-05-18T00:28:57.337114+00:00"}