{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:GDS6JIF5F24F5PPOUY7SDEHPT3","short_pith_number":"pith:GDS6JIF5","schema_version":"1.0","canonical_sha256":"30e5e4a0bd2eb85ebdeea63f2190ef9ef7bdadc0ff826d58a18f3d687b1823ed","source":{"kind":"arxiv","id":"1802.06020","version":1},"attestation_state":"computed","paper":{"title":"On the extremal Betti numbers of binomial edge ideals of block graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Giancarlo Rinaldo, Juergen Herzog","submitted_at":"2018-02-16T16:45:13Z","abstract_excerpt":"We compute one of the distinguished extremal Betti number of the binomial edge ideal of a block graph, and classify all block graphs admitting precisely one 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":"1802.06020","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2018-02-16T16:45:13Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"fde2a2bfbd84ec7a32e25377a94835d51ab5e21e137525424d8674efaebf3510","abstract_canon_sha256":"a428b79a601aa50aef559ef1ea05255da85383b7a1ae257b9f887ebbfa422c52"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:10.130894Z","signature_b64":"5eXmjk//3l+BW8uHWNwKg8v8nh95Sr0/l9/UJeeBRR2fvggdMWWAoDNCdIsjNoi0KRGbF7XUbdwwCS9QpCaPCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"30e5e4a0bd2eb85ebdeea63f2190ef9ef7bdadc0ff826d58a18f3d687b1823ed","last_reissued_at":"2026-05-18T00:23:10.130188Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:10.130188Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the extremal Betti numbers of binomial edge ideals of block graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Giancarlo Rinaldo, Juergen Herzog","submitted_at":"2018-02-16T16:45:13Z","abstract_excerpt":"We compute one of the distinguished extremal Betti number of the binomial edge ideal of a block graph, and classify all block graphs admitting precisely one extremal Betti number."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06020","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":"1802.06020","created_at":"2026-05-18T00:23:10.130301+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.06020v1","created_at":"2026-05-18T00:23:10.130301+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.06020","created_at":"2026-05-18T00:23:10.130301+00:00"},{"alias_kind":"pith_short_12","alias_value":"GDS6JIF5F24F","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_16","alias_value":"GDS6JIF5F24F5PPO","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_8","alias_value":"GDS6JIF5","created_at":"2026-05-18T12:32:25.280505+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/GDS6JIF5F24F5PPOUY7SDEHPT3","json":"https://pith.science/pith/GDS6JIF5F24F5PPOUY7SDEHPT3.json","graph_json":"https://pith.science/api/pith-number/GDS6JIF5F24F5PPOUY7SDEHPT3/graph.json","events_json":"https://pith.science/api/pith-number/GDS6JIF5F24F5PPOUY7SDEHPT3/events.json","paper":"https://pith.science/paper/GDS6JIF5"},"agent_actions":{"view_html":"https://pith.science/pith/GDS6JIF5F24F5PPOUY7SDEHPT3","download_json":"https://pith.science/pith/GDS6JIF5F24F5PPOUY7SDEHPT3.json","view_paper":"https://pith.science/paper/GDS6JIF5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.06020&json=true","fetch_graph":"https://pith.science/api/pith-number/GDS6JIF5F24F5PPOUY7SDEHPT3/graph.json","fetch_events":"https://pith.science/api/pith-number/GDS6JIF5F24F5PPOUY7SDEHPT3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GDS6JIF5F24F5PPOUY7SDEHPT3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GDS6JIF5F24F5PPOUY7SDEHPT3/action/storage_attestation","attest_author":"https://pith.science/pith/GDS6JIF5F24F5PPOUY7SDEHPT3/action/author_attestation","sign_citation":"https://pith.science/pith/GDS6JIF5F24F5PPOUY7SDEHPT3/action/citation_signature","submit_replication":"https://pith.science/pith/GDS6JIF5F24F5PPOUY7SDEHPT3/action/replication_record"}},"created_at":"2026-05-18T00:23:10.130301+00:00","updated_at":"2026-05-18T00:23:10.130301+00:00"}