{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:ULRJWLC6CM3WI2JBI33SV3455P","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f70ff6687e952a44568d8090b515464481d7a932733152eb5a4e663775ca4c2e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-06T02:19:36Z","title_canon_sha256":"6cd1be01537fc202c464692aed8ff09056192951542c426ecbcce378394df5c1"},"schema_version":"1.0","source":{"id":"1508.01263","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.01263","created_at":"2026-05-18T01:33:51Z"},{"alias_kind":"arxiv_version","alias_value":"1508.01263v4","created_at":"2026-05-18T01:33:51Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.01263","created_at":"2026-05-18T01:33:51Z"},{"alias_kind":"pith_short_12","alias_value":"ULRJWLC6CM3W","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_16","alias_value":"ULRJWLC6CM3WI2JB","created_at":"2026-05-18T12:29:44Z"},{"alias_kind":"pith_short_8","alias_value":"ULRJWLC6","created_at":"2026-05-18T12:29:44Z"}],"graph_snapshots":[{"event_id":"sha256:756f873d9735a6f1b92ee6ed750853222a2dee9442160549ce5831a983068e3a","target":"graph","created_at":"2026-05-18T01:33:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Interval minors of bipartite graphs were introduced by Jacob Fox in the study of Stanley-Wilf limits. Recently, Mohar, Rafiey, Tayfeh-Rezaie and Wu investigated the maximum number of edges in $K_{k,\\ell}$-interval minor free bipartite graphs when $k=2$ and $k=3$. In this paper, we investigate the maximum number of edges in $K_{k,\\ell}$-interval minor free bipartite graphs for general $k$ and $\\ell$. We also study the maximum number of edges in $K_{\\ell_1,\\ell_2,\\cdots,\\ell_t}$-interval minor free multipartite graphs.","authors_text":"Hongjian Lai, Yaping Mao, Zhao Wang, Zhiwei Guo","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-06T02:19:36Z","title":"Interval minors of complete multipartite graphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.01263","kind":"arxiv","version":4},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:bcfcd406a9b4905cd9a23fea76cca2c13e52fc5c73285888273775a5d3448941","target":"record","created_at":"2026-05-18T01:33:51Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f70ff6687e952a44568d8090b515464481d7a932733152eb5a4e663775ca4c2e","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2015-08-06T02:19:36Z","title_canon_sha256":"6cd1be01537fc202c464692aed8ff09056192951542c426ecbcce378394df5c1"},"schema_version":"1.0","source":{"id":"1508.01263","kind":"arxiv","version":4}},"canonical_sha256":"a2e29b2c5e133764692146f72aef9debd95e2c1fb9e8ed74857eda7d8b966f05","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a2e29b2c5e133764692146f72aef9debd95e2c1fb9e8ed74857eda7d8b966f05","first_computed_at":"2026-05-18T01:33:51.292001Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:33:51.292001Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"EmUeAJ5CsstjoCrbL83rZ0WhyTiu/gUO+Ga8LXPoaMLdb5I5actaijGZUJCP7TjvnS1Hqz4WvlkCEDwd+IgRDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:33:51.292680Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.01263","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bcfcd406a9b4905cd9a23fea76cca2c13e52fc5c73285888273775a5d3448941","sha256:756f873d9735a6f1b92ee6ed750853222a2dee9442160549ce5831a983068e3a"],"state_sha256":"86867650ccdccb25118889cbb2c1beb853c89f7188b03d42ca6cbbd8ed2050e2"}