{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:SKC43API7CHVWFO3W4GMY34CJZ","short_pith_number":"pith:SKC43API","schema_version":"1.0","canonical_sha256":"9285cd81e8f88f5b15dbb70ccc6f824e52a41e0e938952ac226d22d46bb983b0","source":{"kind":"arxiv","id":"0807.4369","version":3},"attestation_state":"computed","paper":{"title":"Some combinatorial properties of flag simplicial pseudomanifolds and spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christos A. Athanasiadis","submitted_at":"2008-07-28T07:31:31Z","abstract_excerpt":"A simplicial complex $\\Delta$ is called flag if all minimal nonfaces of $\\Delta$ have at most two elements. The following are proved: First, if $\\Delta$ is a flag simplicial pseudomanifold of dimension $d-1$, then the graph of $\\Delta$ (i) is $(2d-2)$-vertex-connected and (ii) has a subgraph which is a subdivision of the graph of the $d$-dimensional cross-polytope. Second, the $h$-vector of a flag simplicial homology sphere $\\Delta$ of dimension $d-1$ is minimized when $\\Delta$ is the boundary complex of the $d$-dimensional cross-polytope."},"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":"0807.4369","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-07-28T07:31:31Z","cross_cats_sorted":[],"title_canon_sha256":"8b70d01be60b904eaaf498678b8980291849023a4001559d59ea42485ed2ac86","abstract_canon_sha256":"a8c8d47d42df1e86fe17c47ca270d375272a6c3a36ca32e2063f363abf92fd19"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:15:44.443237Z","signature_b64":"pN5879T/w9YJSF3GiZASTZMKsBaJFuAbIGDpbg/y/qo4Sx1caB33dEhqyXCfSJeJ5g17JwCgpvKfPNScVZatCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9285cd81e8f88f5b15dbb70ccc6f824e52a41e0e938952ac226d22d46bb983b0","last_reissued_at":"2026-05-18T02:15:44.442658Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:15:44.442658Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Some combinatorial properties of flag simplicial pseudomanifolds and spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Christos A. Athanasiadis","submitted_at":"2008-07-28T07:31:31Z","abstract_excerpt":"A simplicial complex $\\Delta$ is called flag if all minimal nonfaces of $\\Delta$ have at most two elements. The following are proved: First, if $\\Delta$ is a flag simplicial pseudomanifold of dimension $d-1$, then the graph of $\\Delta$ (i) is $(2d-2)$-vertex-connected and (ii) has a subgraph which is a subdivision of the graph of the $d$-dimensional cross-polytope. Second, the $h$-vector of a flag simplicial homology sphere $\\Delta$ of dimension $d-1$ is minimized when $\\Delta$ is the boundary complex of the $d$-dimensional cross-polytope."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0807.4369","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":"0807.4369","created_at":"2026-05-18T02:15:44.442733+00:00"},{"alias_kind":"arxiv_version","alias_value":"0807.4369v3","created_at":"2026-05-18T02:15:44.442733+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0807.4369","created_at":"2026-05-18T02:15:44.442733+00:00"},{"alias_kind":"pith_short_12","alias_value":"SKC43API7CHV","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_16","alias_value":"SKC43API7CHVWFO3","created_at":"2026-05-18T12:25:58.018023+00:00"},{"alias_kind":"pith_short_8","alias_value":"SKC43API","created_at":"2026-05-18T12:25:58.018023+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/SKC43API7CHVWFO3W4GMY34CJZ","json":"https://pith.science/pith/SKC43API7CHVWFO3W4GMY34CJZ.json","graph_json":"https://pith.science/api/pith-number/SKC43API7CHVWFO3W4GMY34CJZ/graph.json","events_json":"https://pith.science/api/pith-number/SKC43API7CHVWFO3W4GMY34CJZ/events.json","paper":"https://pith.science/paper/SKC43API"},"agent_actions":{"view_html":"https://pith.science/pith/SKC43API7CHVWFO3W4GMY34CJZ","download_json":"https://pith.science/pith/SKC43API7CHVWFO3W4GMY34CJZ.json","view_paper":"https://pith.science/paper/SKC43API","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0807.4369&json=true","fetch_graph":"https://pith.science/api/pith-number/SKC43API7CHVWFO3W4GMY34CJZ/graph.json","fetch_events":"https://pith.science/api/pith-number/SKC43API7CHVWFO3W4GMY34CJZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SKC43API7CHVWFO3W4GMY34CJZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SKC43API7CHVWFO3W4GMY34CJZ/action/storage_attestation","attest_author":"https://pith.science/pith/SKC43API7CHVWFO3W4GMY34CJZ/action/author_attestation","sign_citation":"https://pith.science/pith/SKC43API7CHVWFO3W4GMY34CJZ/action/citation_signature","submit_replication":"https://pith.science/pith/SKC43API7CHVWFO3W4GMY34CJZ/action/replication_record"}},"created_at":"2026-05-18T02:15:44.442733+00:00","updated_at":"2026-05-18T02:15:44.442733+00:00"}