{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:WSTF6OPVTAG6J2NAX4A5H3HDQX","short_pith_number":"pith:WSTF6OPV","schema_version":"1.0","canonical_sha256":"b4a65f39f5980de4e9a0bf01d3ece385eddda927280e3ded7e622080e0833555","source":{"kind":"arxiv","id":"1810.00811","version":1},"attestation_state":"computed","paper":{"title":"Caterpillars in Erd\\H{o}s-Hajnal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Anita Liebenau, Marcin Pilipczuk, Paul Seymour, Sophie Spirkl","submitted_at":"2018-10-01T16:48:52Z","abstract_excerpt":"Let $T$ be a tree such that all its vertices of degree more than two lie on one path, that is, $T$ is a caterpillar subdivision. We prove that there exists $\\epsilon>0$ such that for every graph $G$ with $|V(G)|\\ge 2$ not containing $T$ as an induced subgraph, either some vertex has at least $\\epsilon|V(G)|$ neighbours, or there are two disjoint sets of vertices $A,B$, both of cardinality at least $\\epsilon|V(G)|$, where there is no edge joining $A$ and $B$.\n  A consequence is: for every caterpillar subdivision $T$, there exists $c>0$ such that for every graph $G$ containing neither of $T$ and"},"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":"1810.00811","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-01T16:48:52Z","cross_cats_sorted":["cs.DM"],"title_canon_sha256":"2301e71e6b6c96eabce7b63f88eb0497d4c918c9c4a977b26c612027c6022443","abstract_canon_sha256":"125d2292a1124b9f1d4b3adbf2156dbd9bd1351eb9a79f4c34107a4e02763c76"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:24.772755Z","signature_b64":"tOhm9kqhnKmqfjoToIPaMKXVoofvLFU6K8lyoT8kcTv85LuQgrw+mCuucQuI2VFthFUQk9mxyC0uB1WXjnW2BA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b4a65f39f5980de4e9a0bf01d3ece385eddda927280e3ded7e622080e0833555","last_reissued_at":"2026-05-18T00:04:24.772239Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:24.772239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Caterpillars in Erd\\H{o}s-Hajnal","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM"],"primary_cat":"math.CO","authors_text":"Anita Liebenau, Marcin Pilipczuk, Paul Seymour, Sophie Spirkl","submitted_at":"2018-10-01T16:48:52Z","abstract_excerpt":"Let $T$ be a tree such that all its vertices of degree more than two lie on one path, that is, $T$ is a caterpillar subdivision. We prove that there exists $\\epsilon>0$ such that for every graph $G$ with $|V(G)|\\ge 2$ not containing $T$ as an induced subgraph, either some vertex has at least $\\epsilon|V(G)|$ neighbours, or there are two disjoint sets of vertices $A,B$, both of cardinality at least $\\epsilon|V(G)|$, where there is no edge joining $A$ and $B$.\n  A consequence is: for every caterpillar subdivision $T$, there exists $c>0$ such that for every graph $G$ containing neither of $T$ and"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00811","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":"1810.00811","created_at":"2026-05-18T00:04:24.772323+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.00811v1","created_at":"2026-05-18T00:04:24.772323+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.00811","created_at":"2026-05-18T00:04:24.772323+00:00"},{"alias_kind":"pith_short_12","alias_value":"WSTF6OPVTAG6","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_16","alias_value":"WSTF6OPVTAG6J2NA","created_at":"2026-05-18T12:33:01.666342+00:00"},{"alias_kind":"pith_short_8","alias_value":"WSTF6OPV","created_at":"2026-05-18T12:33:01.666342+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/WSTF6OPVTAG6J2NAX4A5H3HDQX","json":"https://pith.science/pith/WSTF6OPVTAG6J2NAX4A5H3HDQX.json","graph_json":"https://pith.science/api/pith-number/WSTF6OPVTAG6J2NAX4A5H3HDQX/graph.json","events_json":"https://pith.science/api/pith-number/WSTF6OPVTAG6J2NAX4A5H3HDQX/events.json","paper":"https://pith.science/paper/WSTF6OPV"},"agent_actions":{"view_html":"https://pith.science/pith/WSTF6OPVTAG6J2NAX4A5H3HDQX","download_json":"https://pith.science/pith/WSTF6OPVTAG6J2NAX4A5H3HDQX.json","view_paper":"https://pith.science/paper/WSTF6OPV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.00811&json=true","fetch_graph":"https://pith.science/api/pith-number/WSTF6OPVTAG6J2NAX4A5H3HDQX/graph.json","fetch_events":"https://pith.science/api/pith-number/WSTF6OPVTAG6J2NAX4A5H3HDQX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WSTF6OPVTAG6J2NAX4A5H3HDQX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WSTF6OPVTAG6J2NAX4A5H3HDQX/action/storage_attestation","attest_author":"https://pith.science/pith/WSTF6OPVTAG6J2NAX4A5H3HDQX/action/author_attestation","sign_citation":"https://pith.science/pith/WSTF6OPVTAG6J2NAX4A5H3HDQX/action/citation_signature","submit_replication":"https://pith.science/pith/WSTF6OPVTAG6J2NAX4A5H3HDQX/action/replication_record"}},"created_at":"2026-05-18T00:04:24.772323+00:00","updated_at":"2026-05-18T00:04:24.772323+00:00"}