{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:EEHDRCOEPFBER6PLEL3RBYJMXD","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":"67dd9d91c5fee99430783673cabdb5d6ac0f7315982dac647683c8ef50e232ca","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-09-14T20:02:01Z","title_canon_sha256":"316d21f7f6db9e182de4ac0708e271c390b524d7c08a0d645e48bf92b1951723"},"schema_version":"1.0","source":{"id":"1009.2756","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1009.2756","created_at":"2026-05-18T02:43:16Z"},{"alias_kind":"arxiv_version","alias_value":"1009.2756v4","created_at":"2026-05-18T02:43:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1009.2756","created_at":"2026-05-18T02:43:16Z"},{"alias_kind":"pith_short_12","alias_value":"EEHDRCOEPFBE","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_16","alias_value":"EEHDRCOEPFBER6PL","created_at":"2026-05-18T12:26:06Z"},{"alias_kind":"pith_short_8","alias_value":"EEHDRCOE","created_at":"2026-05-18T12:26:06Z"}],"graph_snapshots":[{"event_id":"sha256:c0277ecd4f974991e6abfe5a37f2dddfea8566b20e4d2649dca16957caadfec1","target":"graph","created_at":"2026-05-18T02:43:16Z","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 show that the co-chordal cover number of a graph G gives an upper bound for the Castelnuovo-Mumford regularity of the associated edge ideal. Several known combinatorial upper bounds of regularity for edge ideals are then easy consequences of covering results from graph theory, and we derive new upper bounds by looking at additional covering results.","authors_text":"Russ Woodroofe","cross_cats":["math.AC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-09-14T20:02:01Z","title":"Matchings, coverings, and Castelnuovo-Mumford regularity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2756","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":"sha256:8543222ca8f8c45b2efab2165e1e3b5dc391a3377fb9776032fcce1ca1729e89","target":"record","created_at":"2026-05-18T02:43:16Z","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":"67dd9d91c5fee99430783673cabdb5d6ac0f7315982dac647683c8ef50e232ca","cross_cats_sorted":["math.AC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2010-09-14T20:02:01Z","title_canon_sha256":"316d21f7f6db9e182de4ac0708e271c390b524d7c08a0d645e48bf92b1951723"},"schema_version":"1.0","source":{"id":"1009.2756","kind":"arxiv","version":4}},"canonical_sha256":"210e3889c4794248f9eb22f710e12cb8d4468d6b4d198f6602737daa6cb11b3c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"210e3889c4794248f9eb22f710e12cb8d4468d6b4d198f6602737daa6cb11b3c","first_computed_at":"2026-05-18T02:43:16.826337Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:16.826337Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"+9O1RockpV0wPQlrZ0FjukDwcy4udB+qvrk816qHql1wr2SIax0ubzWb43XDv+SnPYMnuplCJIjukRCtI3ZbCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:16.826865Z","signed_message":"canonical_sha256_bytes"},"source_id":"1009.2756","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8543222ca8f8c45b2efab2165e1e3b5dc391a3377fb9776032fcce1ca1729e89","sha256:c0277ecd4f974991e6abfe5a37f2dddfea8566b20e4d2649dca16957caadfec1"],"state_sha256":"e8f0a3d9ba3752e5cd50907aaba85ffaf3b305a590a09aad972f7ce15b51d29c"}