{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:ATRIOZCC7T32CPUYW4QTQ6OAM5","short_pith_number":"pith:ATRIOZCC","schema_version":"1.0","canonical_sha256":"04e2876442fcf7a13e98b7213879c06777e4382cfc524841d16ffe8f306ffb59","source":{"kind":"arxiv","id":"1312.0210","version":1},"attestation_state":"computed","paper":{"title":"Bipartite Minors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Eran Nevo, Gil Kalai, Isabella Novik, Maria Chudnovsky, Paul Seymour","submitted_at":"2013-12-01T12:56:26Z","abstract_excerpt":"We introduce a notion of bipartite minors and prove a bipartite analog of Wagner's theorem: a bipartite graph is planar if and only if it does not contain $K_{3,3}$ as a bipartite minor. Similarly, we provide a forbidden minor characterization for outerplanar graphs and forests. We then establish a recursive characterization of bipartite $(2,2)$-Laman graphs --- a certain family of graphs that contains all maximal bipartite planar graphs."},"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":"1312.0210","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2013-12-01T12:56:26Z","cross_cats_sorted":[],"title_canon_sha256":"8e0bac28f04a12fffbc1b4d460e0d7266b994b75a2575b00a24c9d981e4a17ac","abstract_canon_sha256":"5e5d0e578123b6412a7c3e11f59c9f1ae0f2ba13e426573dc6e98eed28e88750"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:46.362194Z","signature_b64":"MXPuXyj2tUpjchoPK50YD9rvg2XN6AEaLEoVuHmEyfic2Dla6Vp4NuRzGIqUNzhYaalmn7kP1o9Xp0nhZsZeBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"04e2876442fcf7a13e98b7213879c06777e4382cfc524841d16ffe8f306ffb59","last_reissued_at":"2026-05-18T03:05:46.361572Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:46.361572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Bipartite Minors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Eran Nevo, Gil Kalai, Isabella Novik, Maria Chudnovsky, Paul Seymour","submitted_at":"2013-12-01T12:56:26Z","abstract_excerpt":"We introduce a notion of bipartite minors and prove a bipartite analog of Wagner's theorem: a bipartite graph is planar if and only if it does not contain $K_{3,3}$ as a bipartite minor. Similarly, we provide a forbidden minor characterization for outerplanar graphs and forests. We then establish a recursive characterization of bipartite $(2,2)$-Laman graphs --- a certain family of graphs that contains all maximal bipartite planar graphs."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0210","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":"1312.0210","created_at":"2026-05-18T03:05:46.361660+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.0210v1","created_at":"2026-05-18T03:05:46.361660+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.0210","created_at":"2026-05-18T03:05:46.361660+00:00"},{"alias_kind":"pith_short_12","alias_value":"ATRIOZCC7T32","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_16","alias_value":"ATRIOZCC7T32CPUY","created_at":"2026-05-18T12:27:38.830355+00:00"},{"alias_kind":"pith_short_8","alias_value":"ATRIOZCC","created_at":"2026-05-18T12:27:38.830355+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/ATRIOZCC7T32CPUYW4QTQ6OAM5","json":"https://pith.science/pith/ATRIOZCC7T32CPUYW4QTQ6OAM5.json","graph_json":"https://pith.science/api/pith-number/ATRIOZCC7T32CPUYW4QTQ6OAM5/graph.json","events_json":"https://pith.science/api/pith-number/ATRIOZCC7T32CPUYW4QTQ6OAM5/events.json","paper":"https://pith.science/paper/ATRIOZCC"},"agent_actions":{"view_html":"https://pith.science/pith/ATRIOZCC7T32CPUYW4QTQ6OAM5","download_json":"https://pith.science/pith/ATRIOZCC7T32CPUYW4QTQ6OAM5.json","view_paper":"https://pith.science/paper/ATRIOZCC","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.0210&json=true","fetch_graph":"https://pith.science/api/pith-number/ATRIOZCC7T32CPUYW4QTQ6OAM5/graph.json","fetch_events":"https://pith.science/api/pith-number/ATRIOZCC7T32CPUYW4QTQ6OAM5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ATRIOZCC7T32CPUYW4QTQ6OAM5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ATRIOZCC7T32CPUYW4QTQ6OAM5/action/storage_attestation","attest_author":"https://pith.science/pith/ATRIOZCC7T32CPUYW4QTQ6OAM5/action/author_attestation","sign_citation":"https://pith.science/pith/ATRIOZCC7T32CPUYW4QTQ6OAM5/action/citation_signature","submit_replication":"https://pith.science/pith/ATRIOZCC7T32CPUYW4QTQ6OAM5/action/replication_record"}},"created_at":"2026-05-18T03:05:46.361660+00:00","updated_at":"2026-05-18T03:05:46.361660+00:00"}