{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:LNJWHCAVDAYLRBAUMXJV6OXGIU","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":"dec86b36fb17568019698aebb2ba8431ca911d3b362a4b27c96e83cdaef8bbe9","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2008-12-12T13:21:06Z","title_canon_sha256":"2f5ce5cc9eb0bf334e80d7b6f84d7dc668044da5df5eb0085463e1e2a16a9e72"},"schema_version":"1.0","source":{"id":"0812.2366","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0812.2366","created_at":"2026-05-18T01:30:43Z"},{"alias_kind":"arxiv_version","alias_value":"0812.2366v1","created_at":"2026-05-18T01:30:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.2366","created_at":"2026-05-18T01:30:43Z"},{"alias_kind":"pith_short_12","alias_value":"LNJWHCAVDAYL","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"LNJWHCAVDAYLRBAU","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"LNJWHCAV","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:e3e948c3d7ee826571a4f69c7e42420e9551336b00a39312401ed040ec8bafd1","target":"graph","created_at":"2026-05-18T01:30:43Z","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":"We consider Stanley--Reisner rings $k[x_1,...,x_n]/I(\\mc{H})$ where $I(\\mc{H})$ is the edge ideal associated to some particular classes of hypergraphs. For instance, we consider hypergraphs that are natural generalizations of graphs that are lines and cycles, and for these we compute the Betti numbers. We also generalize upon some known results about chordal graphs and study a weak form of shellability.","authors_text":"Eric Emtander, Fatemeh Mohammadi, Somayeh Moradi","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2008-12-12T13:21:06Z","title":"Some algebraic properties of hypergraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.2366","kind":"arxiv","version":1},"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:b547be2da146fb1d5928473d664a5e9f0769b54508e448823688443849efc4ac","target":"record","created_at":"2026-05-18T01:30:43Z","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":"dec86b36fb17568019698aebb2ba8431ca911d3b362a4b27c96e83cdaef8bbe9","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2008-12-12T13:21:06Z","title_canon_sha256":"2f5ce5cc9eb0bf334e80d7b6f84d7dc668044da5df5eb0085463e1e2a16a9e72"},"schema_version":"1.0","source":{"id":"0812.2366","kind":"arxiv","version":1}},"canonical_sha256":"5b536388151830b8841465d35f3ae6452402874b1d6adcad7c3dd756def66c5b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b536388151830b8841465d35f3ae6452402874b1d6adcad7c3dd756def66c5b","first_computed_at":"2026-05-18T01:30:43.643187Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:43.643187Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"myopXR3kztH5b+MjkqyTR1HFVKT4J3dEvbscms/ksZLmfYtvDK810gKXZe1SneOvSTFwnEVupZ/TMr+jPAwLDg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:43.643791Z","signed_message":"canonical_sha256_bytes"},"source_id":"0812.2366","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b547be2da146fb1d5928473d664a5e9f0769b54508e448823688443849efc4ac","sha256:e3e948c3d7ee826571a4f69c7e42420e9551336b00a39312401ed040ec8bafd1"],"state_sha256":"a38c0ac75ca59526f8c5a2c229b213e852f26c1f4f9adc80a6f839f2d22931ed"}