{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2004:SNTGPFDEJQJHTQVUSP6V3JRFAP","short_pith_number":"pith:SNTGPFDE","schema_version":"1.0","canonical_sha256":"93666794644c1279c2b493fd5da62503d990ec3387d27f542cc6020d3493a604","source":{"kind":"arxiv","id":"math/0411488","version":2},"attestation_state":"computed","paper":{"title":"The obstructions for toroidal graphs with no $K_{3,3}$'s","license":"","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Andrei Gagarin, John Chambers, Wendy Myrvold","submitted_at":"2004-11-22T20:33:28Z","abstract_excerpt":"Forbidden minors and subdivisions for toroidal graphs are numerous. We consider the toroidal graphs with no $K_{3,3}$-subdivisions that coincide with the toroidal graphs with no $K_{3,3}$-minors. These graphs admit a unique decomposition into planar components and have short lists of obstructions. We provide the complete lists of four forbidden minors and eleven forbidden subdivisions for the toroidal graphs with no $K_{3,3}$'s and prove that the lists are sufficient."},"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":"math/0411488","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"math.CO","submitted_at":"2004-11-22T20:33:28Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"dc80922b54d5fa554b493c0ca3fde8d09256529735b7c7582b9d5e29e5ba92a0","abstract_canon_sha256":"e92295cf2aee3561b7e0a578d358a714299405f3443130324622594e2e3c7c79"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:32:53.676463Z","signature_b64":"Kbeo8cvazO5T+CWVOmTTXrRovnAQTSwhfnmhLz+RxYSzowEjWPnDForWjmLQkgdVi0TnCEanmDx4nF1wz2nmBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"93666794644c1279c2b493fd5da62503d990ec3387d27f542cc6020d3493a604","last_reissued_at":"2026-05-18T04:32:53.676061Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:32:53.676061Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The obstructions for toroidal graphs with no $K_{3,3}$'s","license":"","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Andrei Gagarin, John Chambers, Wendy Myrvold","submitted_at":"2004-11-22T20:33:28Z","abstract_excerpt":"Forbidden minors and subdivisions for toroidal graphs are numerous. We consider the toroidal graphs with no $K_{3,3}$-subdivisions that coincide with the toroidal graphs with no $K_{3,3}$-minors. These graphs admit a unique decomposition into planar components and have short lists of obstructions. We provide the complete lists of four forbidden minors and eleven forbidden subdivisions for the toroidal graphs with no $K_{3,3}$'s and prove that the lists are sufficient."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0411488","kind":"arxiv","version":2},"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":"math/0411488","created_at":"2026-05-18T04:32:53.676121+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0411488v2","created_at":"2026-05-18T04:32:53.676121+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0411488","created_at":"2026-05-18T04:32:53.676121+00:00"},{"alias_kind":"pith_short_12","alias_value":"SNTGPFDEJQJH","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_16","alias_value":"SNTGPFDEJQJHTQVU","created_at":"2026-05-18T12:25:52.687210+00:00"},{"alias_kind":"pith_short_8","alias_value":"SNTGPFDE","created_at":"2026-05-18T12:25:52.687210+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/SNTGPFDEJQJHTQVUSP6V3JRFAP","json":"https://pith.science/pith/SNTGPFDEJQJHTQVUSP6V3JRFAP.json","graph_json":"https://pith.science/api/pith-number/SNTGPFDEJQJHTQVUSP6V3JRFAP/graph.json","events_json":"https://pith.science/api/pith-number/SNTGPFDEJQJHTQVUSP6V3JRFAP/events.json","paper":"https://pith.science/paper/SNTGPFDE"},"agent_actions":{"view_html":"https://pith.science/pith/SNTGPFDEJQJHTQVUSP6V3JRFAP","download_json":"https://pith.science/pith/SNTGPFDEJQJHTQVUSP6V3JRFAP.json","view_paper":"https://pith.science/paper/SNTGPFDE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0411488&json=true","fetch_graph":"https://pith.science/api/pith-number/SNTGPFDEJQJHTQVUSP6V3JRFAP/graph.json","fetch_events":"https://pith.science/api/pith-number/SNTGPFDEJQJHTQVUSP6V3JRFAP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/SNTGPFDEJQJHTQVUSP6V3JRFAP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/SNTGPFDEJQJHTQVUSP6V3JRFAP/action/storage_attestation","attest_author":"https://pith.science/pith/SNTGPFDEJQJHTQVUSP6V3JRFAP/action/author_attestation","sign_citation":"https://pith.science/pith/SNTGPFDEJQJHTQVUSP6V3JRFAP/action/citation_signature","submit_replication":"https://pith.science/pith/SNTGPFDEJQJHTQVUSP6V3JRFAP/action/replication_record"}},"created_at":"2026-05-18T04:32:53.676121+00:00","updated_at":"2026-05-18T04:32:53.676121+00:00"}