{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:N7JQJTXVQ4YSGYUMEHPGVDP5YR","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":"01c03919afa0d264fa70f69458b16d83c48e085679ebbfb8080a2eb485398193","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-01-24T09:53:29Z","title_canon_sha256":"20e4d63f12dc515b93d66eb9b874f61d4d3e1dff6bbc81f1a5a9693bc912d15f"},"schema_version":"1.0","source":{"id":"1101.4480","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1101.4480","created_at":"2026-05-18T03:49:22Z"},{"alias_kind":"arxiv_version","alias_value":"1101.4480v2","created_at":"2026-05-18T03:49:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1101.4480","created_at":"2026-05-18T03:49:22Z"},{"alias_kind":"pith_short_12","alias_value":"N7JQJTXVQ4YS","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_16","alias_value":"N7JQJTXVQ4YSGYUM","created_at":"2026-05-18T12:26:37Z"},{"alias_kind":"pith_short_8","alias_value":"N7JQJTXV","created_at":"2026-05-18T12:26:37Z"}],"graph_snapshots":[{"event_id":"sha256:6310b790e20b28c157540d69a7a211d03df1152dc83755855226ea4e734e834f","target":"graph","created_at":"2026-05-18T03:49:22Z","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":"Let \\Delta be a (d-1)-dimensional homology sphere on n vertices with m minimal non-faces. We consider the invariant \\alpha := m - (n-d) and prove that for a given value of \\alpha, there are only finitely many homology spheres that cannot be obtained through one-point suspension and suspension from another. Moreover, we describe all homology spheres with \\alpha up to four and, as a corollary, all homology spheres with up to eight minimal non-faces. To prove these results we consider the nerve of the minimal non-faces of \\Delta.","authors_text":"Lukas Katth\\\"an","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-01-24T09:53:29Z","title":"On homology spheres with few minimal non faces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.4480","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":"sha256:6db707a345a3024355979788ee3524425e22fe602709d4b713e0ee4e2825d37a","target":"record","created_at":"2026-05-18T03:49:22Z","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":"01c03919afa0d264fa70f69458b16d83c48e085679ebbfb8080a2eb485398193","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2011-01-24T09:53:29Z","title_canon_sha256":"20e4d63f12dc515b93d66eb9b874f61d4d3e1dff6bbc81f1a5a9693bc912d15f"},"schema_version":"1.0","source":{"id":"1101.4480","kind":"arxiv","version":2}},"canonical_sha256":"6fd304cef5873123628c21de6a8dfdc45967f931ea877d0685fa8e448d7c010d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6fd304cef5873123628c21de6a8dfdc45967f931ea877d0685fa8e448d7c010d","first_computed_at":"2026-05-18T03:49:22.411035Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:22.411035Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TR+9V/COsxts5ULTDwOUTPVz7RBf3VrCm2x15Qso+jvMximsATMGEov8y7mPSYdbi8uxIaavMwYYlj9rvQPXCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:22.411735Z","signed_message":"canonical_sha256_bytes"},"source_id":"1101.4480","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6db707a345a3024355979788ee3524425e22fe602709d4b713e0ee4e2825d37a","sha256:6310b790e20b28c157540d69a7a211d03df1152dc83755855226ea4e734e834f"],"state_sha256":"9ddc823d1985a6913e2cc343860e8d1c1f6a744f664791fe95f881366bf18b9a"}