{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:WSTF6OPVTAG6J2NAX4A5H3HDQX","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":"125d2292a1124b9f1d4b3adbf2156dbd9bd1351eb9a79f4c34107a4e02763c76","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-01T16:48:52Z","title_canon_sha256":"2301e71e6b6c96eabce7b63f88eb0497d4c918c9c4a977b26c612027c6022443"},"schema_version":"1.0","source":{"id":"1810.00811","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.00811","created_at":"2026-05-18T00:04:24Z"},{"alias_kind":"arxiv_version","alias_value":"1810.00811v1","created_at":"2026-05-18T00:04:24Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.00811","created_at":"2026-05-18T00:04:24Z"},{"alias_kind":"pith_short_12","alias_value":"WSTF6OPVTAG6","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_16","alias_value":"WSTF6OPVTAG6J2NA","created_at":"2026-05-18T12:33:01Z"},{"alias_kind":"pith_short_8","alias_value":"WSTF6OPV","created_at":"2026-05-18T12:33:01Z"}],"graph_snapshots":[{"event_id":"sha256:827648017c357b04d929c5b65b77c91c4ed33846b8ad244a32eea1ea60bdb28b","target":"graph","created_at":"2026-05-18T00:04:24Z","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":"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","authors_text":"Anita Liebenau, Marcin Pilipczuk, Paul Seymour, Sophie Spirkl","cross_cats":["cs.DM"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-01T16:48:52Z","title":"Caterpillars in Erd\\H{o}s-Hajnal"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.00811","kind":"arxiv","version":1},"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":"sha256:5a01b3ba3d6ba0137e230e8cc25c014d7c1e627d9453fa9ccb809084c3518452","target":"record","created_at":"2026-05-18T00:04:24Z","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":"125d2292a1124b9f1d4b3adbf2156dbd9bd1351eb9a79f4c34107a4e02763c76","cross_cats_sorted":["cs.DM"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-10-01T16:48:52Z","title_canon_sha256":"2301e71e6b6c96eabce7b63f88eb0497d4c918c9c4a977b26c612027c6022443"},"schema_version":"1.0","source":{"id":"1810.00811","kind":"arxiv","version":1}},"canonical_sha256":"b4a65f39f5980de4e9a0bf01d3ece385eddda927280e3ded7e622080e0833555","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b4a65f39f5980de4e9a0bf01d3ece385eddda927280e3ded7e622080e0833555","first_computed_at":"2026-05-18T00:04:24.772239Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:24.772239Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tOhm9kqhnKmqfjoToIPaMKXVoofvLFU6K8lyoT8kcTv85LuQgrw+mCuucQuI2VFthFUQk9mxyC0uB1WXjnW2BA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:24.772755Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.00811","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5a01b3ba3d6ba0137e230e8cc25c014d7c1e627d9453fa9ccb809084c3518452","sha256:827648017c357b04d929c5b65b77c91c4ed33846b8ad244a32eea1ea60bdb28b"],"state_sha256":"21cc4737f86cf989735af50c271f58c43f32e2638c92d4902d41a764f799f8c1"}