{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2008:CLEDT6TSPDQLER4YCIV6LT36TG","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":"c8ff2d59ae2690565eb4627d150921a56afe98ff5959235caf88aa7087fca0fd","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-08-13T12:00:07Z","title_canon_sha256":"69ffa1134d9c69a5f03aa9ff1cf2f5eb30f035a6c33f2cfb5f3be6f03ece5ca5"},"schema_version":"1.0","source":{"id":"0808.1813","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0808.1813","created_at":"2026-05-18T04:39:17Z"},{"alias_kind":"arxiv_version","alias_value":"0808.1813v1","created_at":"2026-05-18T04:39:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0808.1813","created_at":"2026-05-18T04:39:17Z"},{"alias_kind":"pith_short_12","alias_value":"CLEDT6TSPDQL","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_16","alias_value":"CLEDT6TSPDQLER4Y","created_at":"2026-05-18T12:25:57Z"},{"alias_kind":"pith_short_8","alias_value":"CLEDT6TS","created_at":"2026-05-18T12:25:57Z"}],"graph_snapshots":[{"event_id":"sha256:ff60abd79511db450d0e2083667b26013a377fa0226153f31e8f9b3928bd8ecc","target":"graph","created_at":"2026-05-18T04:39:17Z","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":"Shellability is a well-known combinatorial criterion for verifying that a simplicial complex is Cohen-Macaulay. Another notion familiar to commutative algebraists, but which has not received as much attention from combinatorialists as the Cohen-Macaulay property, is the notion of a Golod ring. Recently, a criterion on simplicial complexes reminiscent of shellability, called the strong gcd-condition, was shown to imply Golodness of the associated Stanley-Reisner ring. The two algebraic notions were tied together by Herzog, Reiner and Welker who showed that if the Alexander dual of a complex is ","authors_text":"Alexander Berglund","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-08-13T12:00:07Z","title":"Shellability and the strong gcd-condition"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0808.1813","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:eefd8ddaa4d870ff5a4a60e29fd2536fa62be45c2ce3fa18ad3ed382a77a26d2","target":"record","created_at":"2026-05-18T04:39:17Z","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":"c8ff2d59ae2690565eb4627d150921a56afe98ff5959235caf88aa7087fca0fd","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2008-08-13T12:00:07Z","title_canon_sha256":"69ffa1134d9c69a5f03aa9ff1cf2f5eb30f035a6c33f2cfb5f3be6f03ece5ca5"},"schema_version":"1.0","source":{"id":"0808.1813","kind":"arxiv","version":1}},"canonical_sha256":"12c839fa7278e0b24798122be5cf7e99a1c483ecbc786af731cb6b4c84cbcb0e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"12c839fa7278e0b24798122be5cf7e99a1c483ecbc786af731cb6b4c84cbcb0e","first_computed_at":"2026-05-18T04:39:17.100972Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:39:17.100972Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"G2gxU7ZNWdOettT+60QpaGDCY6zsqzsEnoNQddSbcxge8oT+6LTqudmPh1fCGf5tGejr1dSpJgraQnxuvSd1AQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:39:17.101674Z","signed_message":"canonical_sha256_bytes"},"source_id":"0808.1813","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eefd8ddaa4d870ff5a4a60e29fd2536fa62be45c2ce3fa18ad3ed382a77a26d2","sha256:ff60abd79511db450d0e2083667b26013a377fa0226153f31e8f9b3928bd8ecc"],"state_sha256":"3224f91056bf27806e79099fc063650fd826fe6b82ee2cdfcde629efe7fce6b1"}