{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:DPN6V5LW2MJ4MGQUQMZE52NAED","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":"e9b5cc0b84abe6ca7ff63d14b95f8929b559ef7b595ed417fdae8039d946e4cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-10-15T09:45:51Z","title_canon_sha256":"ad41b8517bd12d5986b69a575a7db971ba92bfc6a30c92877732f419160f6b4d"},"schema_version":"1.0","source":{"id":"1310.3981","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.3981","created_at":"2026-05-18T03:10:25Z"},{"alias_kind":"arxiv_version","alias_value":"1310.3981v1","created_at":"2026-05-18T03:10:25Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.3981","created_at":"2026-05-18T03:10:25Z"},{"alias_kind":"pith_short_12","alias_value":"DPN6V5LW2MJ4","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"DPN6V5LW2MJ4MGQU","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"DPN6V5LW","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:69a12d2d9320474fce57fa5f3c37aa3a480592dee22b840543d71cea45469ad3","target":"graph","created_at":"2026-05-18T03:10:25Z","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 study the Betti numbers of binomial edge ideal associated to some classes of graphs with large Castelnuovo-Mumford regularity. As an application we give several lower bounds of the Castelnuovo-Mumford regularity of arbitrary graphs depending on induced subgraphs.","authors_text":"Sohail Zafar, Zohaib Zahid","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-10-15T09:45:51Z","title":"On the Betti numbers of some classes of Binomial edge ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3981","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:cd12fe55f3898de103e9bd345baf2bea542d3605c9e2ebdc97f0b1adf1f9201e","target":"record","created_at":"2026-05-18T03:10:25Z","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":"e9b5cc0b84abe6ca7ff63d14b95f8929b559ef7b595ed417fdae8039d946e4cf","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-10-15T09:45:51Z","title_canon_sha256":"ad41b8517bd12d5986b69a575a7db971ba92bfc6a30c92877732f419160f6b4d"},"schema_version":"1.0","source":{"id":"1310.3981","kind":"arxiv","version":1}},"canonical_sha256":"1bdbeaf576d313c61a1483324ee9a020dd553065c4d31f477832ab412a109573","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1bdbeaf576d313c61a1483324ee9a020dd553065c4d31f477832ab412a109573","first_computed_at":"2026-05-18T03:10:25.528188Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:10:25.528188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zSSV7tClMFGsnI8/4EVCmUn6Vwj5ChC2kRULORGQM+hzjt43F7iXfCpW0uvdzE506f182evsT1uycOH6peZQAQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:10:25.528844Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.3981","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cd12fe55f3898de103e9bd345baf2bea542d3605c9e2ebdc97f0b1adf1f9201e","sha256:69a12d2d9320474fce57fa5f3c37aa3a480592dee22b840543d71cea45469ad3"],"state_sha256":"a3312f8cb3bd9c3c59c641ec1fda1cd3f525e3c3d14407f492a943ca8b516a7c"}