{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:CVSHJKN2SPAVZIYJTGDEEHPRR7","short_pith_number":"pith:CVSHJKN2","schema_version":"1.0","canonical_sha256":"156474a9ba93c15ca3099986421df18fe88119cd69b794d4cd00cc32dbfa394c","source":{"kind":"arxiv","id":"1210.8069","version":3},"attestation_state":"computed","paper":{"title":"Betti diagrams from graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"Alexander Engstr\\\"om, Matthew T. Stamps","submitted_at":"2012-10-30T16:18:22Z","abstract_excerpt":"The emergence of Boij-S\\\"oderberg theory has given rise to new connections between combinatorics and commutative algebra. Herzog, Sharifan, and Varbaro recently showed that every Betti diagram of an ideal with a k-linear minimal resolution arises from that of the Stanley-Reisner ideal of a simplicial complex. In this paper, we extend their result for the special case of 2-linear resolutions using purely combinatorial methods. Specifically, we show bijective correspondences between Betti diagrams of ideals with 2-linear resolutions, threshold graphs, and anti-lecture hall compositions. Moreover"},"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":"1210.8069","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2012-10-30T16:18:22Z","cross_cats_sorted":["math.AC"],"title_canon_sha256":"0b20674ab56d58be1c94cd231afd753ae3bb6267565addf90248f5efc2bc1683","abstract_canon_sha256":"b785d14fc4561b1f121116a9932a9f55f41d5ca3e3318fd57a0cff5ea72b5cf4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:22:26.075058Z","signature_b64":"4pyCCG6HF8NC+umu47VyRWoS59VwfOcH7Sn3Kvz8k5ES75+ESSCpB2/WqbUDwi5YIUKJwUZvP/ArO1O5eoMIDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"156474a9ba93c15ca3099986421df18fe88119cd69b794d4cd00cc32dbfa394c","last_reissued_at":"2026-05-18T01:22:26.074413Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:22:26.074413Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Betti diagrams from graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC"],"primary_cat":"math.CO","authors_text":"Alexander Engstr\\\"om, Matthew T. Stamps","submitted_at":"2012-10-30T16:18:22Z","abstract_excerpt":"The emergence of Boij-S\\\"oderberg theory has given rise to new connections between combinatorics and commutative algebra. Herzog, Sharifan, and Varbaro recently showed that every Betti diagram of an ideal with a k-linear minimal resolution arises from that of the Stanley-Reisner ideal of a simplicial complex. In this paper, we extend their result for the special case of 2-linear resolutions using purely combinatorial methods. Specifically, we show bijective correspondences between Betti diagrams of ideals with 2-linear resolutions, threshold graphs, and anti-lecture hall compositions. Moreover"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.8069","kind":"arxiv","version":3},"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":"1210.8069","created_at":"2026-05-18T01:22:26.074507+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.8069v3","created_at":"2026-05-18T01:22:26.074507+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.8069","created_at":"2026-05-18T01:22:26.074507+00:00"},{"alias_kind":"pith_short_12","alias_value":"CVSHJKN2SPAV","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_16","alias_value":"CVSHJKN2SPAVZIYJ","created_at":"2026-05-18T12:27:01.376967+00:00"},{"alias_kind":"pith_short_8","alias_value":"CVSHJKN2","created_at":"2026-05-18T12:27:01.376967+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/CVSHJKN2SPAVZIYJTGDEEHPRR7","json":"https://pith.science/pith/CVSHJKN2SPAVZIYJTGDEEHPRR7.json","graph_json":"https://pith.science/api/pith-number/CVSHJKN2SPAVZIYJTGDEEHPRR7/graph.json","events_json":"https://pith.science/api/pith-number/CVSHJKN2SPAVZIYJTGDEEHPRR7/events.json","paper":"https://pith.science/paper/CVSHJKN2"},"agent_actions":{"view_html":"https://pith.science/pith/CVSHJKN2SPAVZIYJTGDEEHPRR7","download_json":"https://pith.science/pith/CVSHJKN2SPAVZIYJTGDEEHPRR7.json","view_paper":"https://pith.science/paper/CVSHJKN2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.8069&json=true","fetch_graph":"https://pith.science/api/pith-number/CVSHJKN2SPAVZIYJTGDEEHPRR7/graph.json","fetch_events":"https://pith.science/api/pith-number/CVSHJKN2SPAVZIYJTGDEEHPRR7/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/CVSHJKN2SPAVZIYJTGDEEHPRR7/action/timestamp_anchor","attest_storage":"https://pith.science/pith/CVSHJKN2SPAVZIYJTGDEEHPRR7/action/storage_attestation","attest_author":"https://pith.science/pith/CVSHJKN2SPAVZIYJTGDEEHPRR7/action/author_attestation","sign_citation":"https://pith.science/pith/CVSHJKN2SPAVZIYJTGDEEHPRR7/action/citation_signature","submit_replication":"https://pith.science/pith/CVSHJKN2SPAVZIYJTGDEEHPRR7/action/replication_record"}},"created_at":"2026-05-18T01:22:26.074507+00:00","updated_at":"2026-05-18T01:22:26.074507+00:00"}