{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:GC6NVS3XAGVDVAEDUBIP3TZISE","short_pith_number":"pith:GC6NVS3X","schema_version":"1.0","canonical_sha256":"30bcdacb7701aa3a8083a050fdcf289137059ef680de78cd152826cf061acd1e","source":{"kind":"arxiv","id":"1701.08857","version":1},"attestation_state":"computed","paper":{"title":"Infinitely many minimal classes of graphs of unbounded clique-width","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"A. Collins, J. Foniok, N. Korpelainen, V. Lozin, V. Zamaraev","submitted_at":"2017-01-30T22:27:19Z","abstract_excerpt":"The celebrated theorem of Robertson and Seymour states that in the family of minor-closed graph classes, there is a unique minimal class of graphs of unbounded tree-width, namely, the class of planar graphs. In the case of tree-width, the restriction to minor-closed classes is justified by the fact that the tree-width of a graph is never smaller than the tree-width of any of its minors. This, however, is not the case with respect to clique-width, as the clique-width of a graph can be (much) smaller than the clique-width of its minor. On the other hand, the clique-width of a graph is never smal"},"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":"1701.08857","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2017-01-30T22:27:19Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"6b84e6c1a8167b518e17a042afe451167b9de6cdecfa6378854120dd0d076ab4","abstract_canon_sha256":"9fda0a4a61ff6f279797c38e5043409f93846c3deb0896c1abc95de2565655b9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:51:39.006534Z","signature_b64":"kmCqafDTO01I/G6GbliBwbqmnvEhYyTnT0I9/9xhwpdS50j++umG4U/C4J5gRch17CL9PMkj7/HrbWQ/KULwBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"30bcdacb7701aa3a8083a050fdcf289137059ef680de78cd152826cf061acd1e","last_reissued_at":"2026-05-18T00:51:39.006120Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:51:39.006120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Infinitely many minimal classes of graphs of unbounded clique-width","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"A. Collins, J. Foniok, N. Korpelainen, V. Lozin, V. Zamaraev","submitted_at":"2017-01-30T22:27:19Z","abstract_excerpt":"The celebrated theorem of Robertson and Seymour states that in the family of minor-closed graph classes, there is a unique minimal class of graphs of unbounded tree-width, namely, the class of planar graphs. In the case of tree-width, the restriction to minor-closed classes is justified by the fact that the tree-width of a graph is never smaller than the tree-width of any of its minors. This, however, is not the case with respect to clique-width, as the clique-width of a graph can be (much) smaller than the clique-width of its minor. On the other hand, the clique-width of a graph is never smal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.08857","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":"1701.08857","created_at":"2026-05-18T00:51:39.006180+00:00"},{"alias_kind":"arxiv_version","alias_value":"1701.08857v1","created_at":"2026-05-18T00:51:39.006180+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.08857","created_at":"2026-05-18T00:51:39.006180+00:00"},{"alias_kind":"pith_short_12","alias_value":"GC6NVS3XAGVD","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_16","alias_value":"GC6NVS3XAGVDVAED","created_at":"2026-05-18T12:31:15.632608+00:00"},{"alias_kind":"pith_short_8","alias_value":"GC6NVS3X","created_at":"2026-05-18T12:31:15.632608+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/GC6NVS3XAGVDVAEDUBIP3TZISE","json":"https://pith.science/pith/GC6NVS3XAGVDVAEDUBIP3TZISE.json","graph_json":"https://pith.science/api/pith-number/GC6NVS3XAGVDVAEDUBIP3TZISE/graph.json","events_json":"https://pith.science/api/pith-number/GC6NVS3XAGVDVAEDUBIP3TZISE/events.json","paper":"https://pith.science/paper/GC6NVS3X"},"agent_actions":{"view_html":"https://pith.science/pith/GC6NVS3XAGVDVAEDUBIP3TZISE","download_json":"https://pith.science/pith/GC6NVS3XAGVDVAEDUBIP3TZISE.json","view_paper":"https://pith.science/paper/GC6NVS3X","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1701.08857&json=true","fetch_graph":"https://pith.science/api/pith-number/GC6NVS3XAGVDVAEDUBIP3TZISE/graph.json","fetch_events":"https://pith.science/api/pith-number/GC6NVS3XAGVDVAEDUBIP3TZISE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GC6NVS3XAGVDVAEDUBIP3TZISE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GC6NVS3XAGVDVAEDUBIP3TZISE/action/storage_attestation","attest_author":"https://pith.science/pith/GC6NVS3XAGVDVAEDUBIP3TZISE/action/author_attestation","sign_citation":"https://pith.science/pith/GC6NVS3XAGVDVAEDUBIP3TZISE/action/citation_signature","submit_replication":"https://pith.science/pith/GC6NVS3XAGVDVAEDUBIP3TZISE/action/replication_record"}},"created_at":"2026-05-18T00:51:39.006180+00:00","updated_at":"2026-05-18T00:51:39.006180+00:00"}