{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:4737US3TVSI6MALJJCPXTNASVF","short_pith_number":"pith:4737US3T","schema_version":"1.0","canonical_sha256":"e7f7fa4b73ac91e60169489f79b412a94bd9003246e4f96efb8f507dbfd17e20","source":{"kind":"arxiv","id":"1310.2903","version":1},"attestation_state":"computed","paper":{"title":"Extremal Betti numbers of some classes of binomial edge ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Ahmet Dokuyucu","submitted_at":"2013-10-10T18:14:58Z","abstract_excerpt":"Let $G$ be a cycle or a complete bipartite graph. We show that the binomial edge ideal $J_{G}$ and its initial ideal with respect to the lexicographic order have the same extremal Betti number."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1310.2903","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2013-10-10T18:14:58Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"bdcd51969d1101e1b9f7ac70d5def60dfac8a6a2bd5dca160bb08b18cafb4685","abstract_canon_sha256":"455cf356a1768ee9fd724671c7bb5a269c4565bbe8e004619199a0a82db46a5a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:10:46.361830Z","signature_b64":"EOeYs2C12bVizkuMKm6N7lNuXkJdzb1L6aWej9uYTIgNHOPm61CTL6ny5ia045Mi+4fxwds1ZLHu9Rew5q83AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7f7fa4b73ac91e60169489f79b412a94bd9003246e4f96efb8f507dbfd17e20","last_reissued_at":"2026-05-18T03:10:46.361233Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:10:46.361233Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extremal Betti numbers of some classes of binomial edge ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Ahmet Dokuyucu","submitted_at":"2013-10-10T18:14:58Z","abstract_excerpt":"Let $G$ be a cycle or a complete bipartite graph. We show that the binomial edge ideal $J_{G}$ and its initial ideal with respect to the lexicographic order have the same extremal Betti number."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2903","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1310.2903","created_at":"2026-05-18T03:10:46.361355+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.2903v1","created_at":"2026-05-18T03:10:46.361355+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.2903","created_at":"2026-05-18T03:10:46.361355+00:00"},{"alias_kind":"pith_short_12","alias_value":"4737US3TVSI6","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_16","alias_value":"4737US3TVSI6MALJ","created_at":"2026-05-18T12:27:32.513160+00:00"},{"alias_kind":"pith_short_8","alias_value":"4737US3T","created_at":"2026-05-18T12:27:32.513160+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4737US3TVSI6MALJJCPXTNASVF","json":"https://pith.science/pith/4737US3TVSI6MALJJCPXTNASVF.json","graph_json":"https://pith.science/api/pith-number/4737US3TVSI6MALJJCPXTNASVF/graph.json","events_json":"https://pith.science/api/pith-number/4737US3TVSI6MALJJCPXTNASVF/events.json","paper":"https://pith.science/paper/4737US3T"},"agent_actions":{"view_html":"https://pith.science/pith/4737US3TVSI6MALJJCPXTNASVF","download_json":"https://pith.science/pith/4737US3TVSI6MALJJCPXTNASVF.json","view_paper":"https://pith.science/paper/4737US3T","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.2903&json=true","fetch_graph":"https://pith.science/api/pith-number/4737US3TVSI6MALJJCPXTNASVF/graph.json","fetch_events":"https://pith.science/api/pith-number/4737US3TVSI6MALJJCPXTNASVF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4737US3TVSI6MALJJCPXTNASVF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4737US3TVSI6MALJJCPXTNASVF/action/storage_attestation","attest_author":"https://pith.science/pith/4737US3TVSI6MALJJCPXTNASVF/action/author_attestation","sign_citation":"https://pith.science/pith/4737US3TVSI6MALJJCPXTNASVF/action/citation_signature","submit_replication":"https://pith.science/pith/4737US3TVSI6MALJJCPXTNASVF/action/replication_record"}},"created_at":"2026-05-18T03:10:46.361355+00:00","updated_at":"2026-05-18T03:10:46.361355+00:00"}