{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2002:XYIFQ46CNI6OJ2LAIAP6YDFMBE","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":"961e57737b59a3823b2d3e16fc4be74d58048bb1dc2b9dbce77fadb941fe25e4","cross_cats_sorted":["math.CO"],"license":"","primary_cat":"math.AG","submitted_at":"2002-09-06T12:40:07Z","title_canon_sha256":"87e813bdbf50ec27154c497d1e4c094d7a189f637923357019de44fa9b48c6c5"},"schema_version":"1.0","source":{"id":"math/0209061","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0209061","created_at":"2026-05-18T04:06:21Z"},{"alias_kind":"arxiv_version","alias_value":"math/0209061v4","created_at":"2026-05-18T04:06:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0209061","created_at":"2026-05-18T04:06:21Z"},{"alias_kind":"pith_short_12","alias_value":"XYIFQ46CNI6O","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_16","alias_value":"XYIFQ46CNI6OJ2LA","created_at":"2026-05-18T12:25:51Z"},{"alias_kind":"pith_short_8","alias_value":"XYIFQ46C","created_at":"2026-05-18T12:25:51Z"}],"graph_snapshots":[{"event_id":"sha256:c4579f1f34ff3f35d904d6f3bbb2ba84e04da793d03717978a8cf4f116650af8","target":"graph","created_at":"2026-05-18T04:06:21Z","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":"Via the BGG correspondence a simplicial complex Delta on [n] is transformed into a complex of coherent sheaves on P^n-1. We show that this complex reduces to a coherent sheaf F exactly when the Alexander dual Delta^* is Cohen-Macaulay. We then determine when both Delta and Delta^* are Cohen-Macaulay. This corresponds to F being a locally Cohen-Macaulay sheaf. Lastly we conjecture for which range of invariants of such Delta it must be a cone.","authors_text":"Gunnar Floystad, Jon Eivind Vatne","cross_cats":["math.CO"],"headline":"","license":"","primary_cat":"math.AG","submitted_at":"2002-09-06T12:40:07Z","title":"(Bi-)Cohen-Macaulay simplicial complexes and their associated coherent sheaves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0209061","kind":"arxiv","version":4},"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":"sha256:94b0270a456753f9d0da87a05e4c06907cfb1b04fb83b83aef906b2f2d3a6850","target":"record","created_at":"2026-05-18T04:06:21Z","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":"961e57737b59a3823b2d3e16fc4be74d58048bb1dc2b9dbce77fadb941fe25e4","cross_cats_sorted":["math.CO"],"license":"","primary_cat":"math.AG","submitted_at":"2002-09-06T12:40:07Z","title_canon_sha256":"87e813bdbf50ec27154c497d1e4c094d7a189f637923357019de44fa9b48c6c5"},"schema_version":"1.0","source":{"id":"math/0209061","kind":"arxiv","version":4}},"canonical_sha256":"be105873c26a3ce4e960401fec0cac092286cbc8dc1513fdadc5aac3c09dce8f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"be105873c26a3ce4e960401fec0cac092286cbc8dc1513fdadc5aac3c09dce8f","first_computed_at":"2026-05-18T04:06:21.496193Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:21.496193Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"2jkz0iex1Eg2KHXlwF92yOzN/DWflXbVOgQS5XCdFn1sujN5i6zHZD7/Uiv8PNEhVhVgeEVJcKvlLTJf+oqRCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:21.496976Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0209061","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:94b0270a456753f9d0da87a05e4c06907cfb1b04fb83b83aef906b2f2d3a6850","sha256:c4579f1f34ff3f35d904d6f3bbb2ba84e04da793d03717978a8cf4f116650af8"],"state_sha256":"80665659160f4703b184762d81934386e15d6ba8b484b73cc1ca9cab3c13deaa"}