{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:2TOHINKBBUZ4DYHKGVMM6O4UL7","short_pith_number":"pith:2TOHINKB","schema_version":"1.0","canonical_sha256":"d4dc7435410d33c1e0ea3558cf3b945ffb9c2c0c13947e7f0546f16aed5e7800","source":{"kind":"arxiv","id":"1404.4239","version":3},"attestation_state":"computed","paper":{"title":"Extremal examples of collapsible complexes and random discrete Morse theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","math.AT","math.GT"],"primary_cat":"math.CO","authors_text":"Bruno Benedetti, Frank H. Lutz, Karim A. Adiprasito","submitted_at":"2014-04-16T13:36:00Z","abstract_excerpt":"We present extremal constructions connected with the property of simplicial collapsibility.\n  (1) For each $d \\ge 2$, there are collapsible (and shellable) simplicial $d$-complexes with only one free face. Also, there are non-evasive $d$-complexes with only two free faces. (Both results are optimal in all dimensions.)\n  (2) Optimal discrete Morse vectors need not be unique. We explicitly construct a contractible, but non-collapsible $3$-dimensional simplicial complex with face vector $f=(106,596,1064,573)$ that admits two distinct optimal discrete Morse vectors, $(1,1,1,0)$ and $(1,0,1,1)$. In"},"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":"1404.4239","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2014-04-16T13:36:00Z","cross_cats_sorted":["cs.CG","math.AT","math.GT"],"title_canon_sha256":"e5d92a66611f326fd12a6199ff9420148ed2717075ad098c3349427c9dc6f43b","abstract_canon_sha256":"5950424e832e04532856279cec3142d8c88300479e00bd4fd02002502521af32"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:02:46.088723Z","signature_b64":"OoE7iIOyStnZbSKMggO9rpDfzkUY3HHJKdDYuQm7ClrdsMn8pxeoqsA1amfIpvRMKJMNuhbUtyIb8PFY1XsADA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d4dc7435410d33c1e0ea3558cf3b945ffb9c2c0c13947e7f0546f16aed5e7800","last_reissued_at":"2026-05-18T01:02:46.088294Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:02:46.088294Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extremal examples of collapsible complexes and random discrete Morse theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG","math.AT","math.GT"],"primary_cat":"math.CO","authors_text":"Bruno Benedetti, Frank H. Lutz, Karim A. Adiprasito","submitted_at":"2014-04-16T13:36:00Z","abstract_excerpt":"We present extremal constructions connected with the property of simplicial collapsibility.\n  (1) For each $d \\ge 2$, there are collapsible (and shellable) simplicial $d$-complexes with only one free face. Also, there are non-evasive $d$-complexes with only two free faces. (Both results are optimal in all dimensions.)\n  (2) Optimal discrete Morse vectors need not be unique. We explicitly construct a contractible, but non-collapsible $3$-dimensional simplicial complex with face vector $f=(106,596,1064,573)$ that admits two distinct optimal discrete Morse vectors, $(1,1,1,0)$ and $(1,0,1,1)$. In"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.4239","kind":"arxiv","version":3},"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":"1404.4239","created_at":"2026-05-18T01:02:46.088362+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.4239v3","created_at":"2026-05-18T01:02:46.088362+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.4239","created_at":"2026-05-18T01:02:46.088362+00:00"},{"alias_kind":"pith_short_12","alias_value":"2TOHINKBBUZ4","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"2TOHINKBBUZ4DYHK","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"2TOHINKB","created_at":"2026-05-18T12:28:11.866339+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/2TOHINKBBUZ4DYHKGVMM6O4UL7","json":"https://pith.science/pith/2TOHINKBBUZ4DYHKGVMM6O4UL7.json","graph_json":"https://pith.science/api/pith-number/2TOHINKBBUZ4DYHKGVMM6O4UL7/graph.json","events_json":"https://pith.science/api/pith-number/2TOHINKBBUZ4DYHKGVMM6O4UL7/events.json","paper":"https://pith.science/paper/2TOHINKB"},"agent_actions":{"view_html":"https://pith.science/pith/2TOHINKBBUZ4DYHKGVMM6O4UL7","download_json":"https://pith.science/pith/2TOHINKBBUZ4DYHKGVMM6O4UL7.json","view_paper":"https://pith.science/paper/2TOHINKB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.4239&json=true","fetch_graph":"https://pith.science/api/pith-number/2TOHINKBBUZ4DYHKGVMM6O4UL7/graph.json","fetch_events":"https://pith.science/api/pith-number/2TOHINKBBUZ4DYHKGVMM6O4UL7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2TOHINKBBUZ4DYHKGVMM6O4UL7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2TOHINKBBUZ4DYHKGVMM6O4UL7/action/storage_attestation","attest_author":"https://pith.science/pith/2TOHINKBBUZ4DYHKGVMM6O4UL7/action/author_attestation","sign_citation":"https://pith.science/pith/2TOHINKBBUZ4DYHKGVMM6O4UL7/action/citation_signature","submit_replication":"https://pith.science/pith/2TOHINKBBUZ4DYHKGVMM6O4UL7/action/replication_record"}},"created_at":"2026-05-18T01:02:46.088362+00:00","updated_at":"2026-05-18T01:02:46.088362+00:00"}