{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:JNZ35YEJJK2ZKIDMFD2IENR3O6","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":"5b1c7b14bd7bde2f6571625b4f78f6fe4aa7787e20ac88e4b1f6c3c4524ba1dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2009-01-12T10:08:55Z","title_canon_sha256":"58844be7448a5e362c000a0515f744dd690b867f25533114394bc071d5e54f4e"},"schema_version":"1.0","source":{"id":"0901.1534","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0901.1534","created_at":"2026-05-18T01:30:43Z"},{"alias_kind":"arxiv_version","alias_value":"0901.1534v1","created_at":"2026-05-18T01:30:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0901.1534","created_at":"2026-05-18T01:30:43Z"},{"alias_kind":"pith_short_12","alias_value":"JNZ35YEJJK2Z","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"JNZ35YEJJK2ZKIDM","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"JNZ35YEJ","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:14edc4c943a1bf1dcfb20b729f71fb72cb8f661a6705bdc291fea9ff7b8d3f33","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":"A hypergraph $H=(V,E)$, where $V=\\{x_1,...,x_n\\}$ and $E\\subseteq 2^V$ defines a hypergraph algebra $R_H=k[x_1,...,x_n]/(x_{i_1}... x_{i_k}; \\{i_1,...,i_k\\}\\in E)$. All our hypergraphs are $d$-uniform, i.e., $|e_i|=d$ for all $e_i\\in E$. We determine the Poincar\\'e series $P_{R_H}(t)=\\sum_{i=1}^\\infty\\dim_k{\\rm Tor}_i^{R_H}(k,k)t^i$ for some hypergraphs generalizing lines, cycles, and stars. We finish by calculating the graded Betti numbers and the Poincar\\'e series of the graph algebra of the wheel graph.","authors_text":"Eric Emtander, Fatemeh Mohammadi, Ralf Fr\\\"oberg, Somayeh Moradi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2009-01-12T10:08:55Z","title":"Poincar\\'e series of some hypergraph algebras"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0901.1534","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:a3827b852606d5413cdbe2b33262b5f71623280853973264a1982bf396d6ff4e","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":"5b1c7b14bd7bde2f6571625b4f78f6fe4aa7787e20ac88e4b1f6c3c4524ba1dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2009-01-12T10:08:55Z","title_canon_sha256":"58844be7448a5e362c000a0515f744dd690b867f25533114394bc071d5e54f4e"},"schema_version":"1.0","source":{"id":"0901.1534","kind":"arxiv","version":1}},"canonical_sha256":"4b73bee0894ab595206c28f482363b77b6b79b96dd095cf7b84d56f7cd5264f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4b73bee0894ab595206c28f482363b77b6b79b96dd095cf7b84d56f7cd5264f3","first_computed_at":"2026-05-18T01:30:43.634375Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:30:43.634375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"a22Tg1F/Pi+n3g+iNk8BIdbSHQtssawR+R5WF6zID6u5Kb1Sts4VpqmK29Rijn2u/lSWlH4/+1fH39TwYS2LCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:30:43.636502Z","signed_message":"canonical_sha256_bytes"},"source_id":"0901.1534","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3827b852606d5413cdbe2b33262b5f71623280853973264a1982bf396d6ff4e","sha256:14edc4c943a1bf1dcfb20b729f71fb72cb8f661a6705bdc291fea9ff7b8d3f33"],"state_sha256":"359854deb22366c65af47f99abedc50a6a29d9ae22b7bd17e2b1efdd6f4e33d5"}