{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:RPIWTQ4CDWL3QAHRR6R4IELSQJ","short_pith_number":"pith:RPIWTQ4C","canonical_record":{"source":{"id":"1804.11008","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-30T00:35:06Z","cross_cats_sorted":[],"title_canon_sha256":"838b337c3bea5ecb759522a21950f6fb1d5e04df68f2f535a1010101a277777d","abstract_canon_sha256":"c5d06d5fb78cc12c20ea7e816cb029202d92b53748b5a0ec4fb50578c1202efe"},"schema_version":"1.0"},"canonical_sha256":"8bd169c3821d97b800f18fa3c4117282431049ee42f382b2879a060384a872c2","source":{"kind":"arxiv","id":"1804.11008","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.11008","created_at":"2026-05-18T00:04:07Z"},{"alias_kind":"arxiv_version","alias_value":"1804.11008v2","created_at":"2026-05-18T00:04:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.11008","created_at":"2026-05-18T00:04:07Z"},{"alias_kind":"pith_short_12","alias_value":"RPIWTQ4CDWL3","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RPIWTQ4CDWL3QAHR","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RPIWTQ4C","created_at":"2026-05-18T12:32:50Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:RPIWTQ4CDWL3QAHRR6R4IELSQJ","target":"record","payload":{"canonical_record":{"source":{"id":"1804.11008","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-30T00:35:06Z","cross_cats_sorted":[],"title_canon_sha256":"838b337c3bea5ecb759522a21950f6fb1d5e04df68f2f535a1010101a277777d","abstract_canon_sha256":"c5d06d5fb78cc12c20ea7e816cb029202d92b53748b5a0ec4fb50578c1202efe"},"schema_version":"1.0"},"canonical_sha256":"8bd169c3821d97b800f18fa3c4117282431049ee42f382b2879a060384a872c2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:07.737542Z","signature_b64":"KoZSyghMcZppUIpWgTbCOcM2nNuQbv+D0UBK1Uy3NUJeerQitN6oKgiW5ti72my+S2QOhzW9RD4xQ7WZaSigCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8bd169c3821d97b800f18fa3c4117282431049ee42f382b2879a060384a872c2","last_reissued_at":"2026-05-18T00:04:07.736847Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:07.736847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1804.11008","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:04:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+UUcfPTDQFjd9LvHuL0rKG73RUJk5CsQ92yRoyB+zfZm4IT7SCP0FtD5KaV9rFkpyK2iisGfpPqYqtWl2VUqCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:52:56.872591Z"},"content_sha256":"286242179f11f549bf9c6e72756a7ec1c7fc6200b71cf61a08d445505c2bed1b","schema_version":"1.0","event_id":"sha256:286242179f11f549bf9c6e72756a7ec1c7fc6200b71cf61a08d445505c2bed1b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:RPIWTQ4CDWL3QAHRR6R4IELSQJ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Vertex-minors and the Erd\\H{o}s-Hajnal conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CO","authors_text":"Maria Chudnovsky, Sang-il Oum","submitted_at":"2018-04-30T00:35:06Z","abstract_excerpt":"We prove that for every graph $H$, there exists $\\varepsilon>0$ such that every $n$-vertex graph with no vertex-minors isomorphic to $H$ has a pair of disjoint sets $A$, $B$ of vertices such that $|A|, |B|\\ge \\varepsilon n$ and $A$ is complete or anticomplete to $B$. We deduce this from recent work of Chudnovsky, Scott, Seymour, and Spirkl (2018). This proves the analog of the Erd\\H{o}s-Hajnal conjecture for vertex-minors."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.11008","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:04:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"BOzyIXs1MMpbOk1efqzeoyeHH8dsQ3LHwDlZnMEQv9e4ZCZtatLW3+H+Dt4+4gZkdwzhdgeFiLl9HQ1qXlUUCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T08:52:56.873259Z"},"content_sha256":"3bf9f51cb48d3da65030c81901faf78744176dc88e1bbfc4081f9fecf79891c9","schema_version":"1.0","event_id":"sha256:3bf9f51cb48d3da65030c81901faf78744176dc88e1bbfc4081f9fecf79891c9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RPIWTQ4CDWL3QAHRR6R4IELSQJ/bundle.json","state_url":"https://pith.science/pith/RPIWTQ4CDWL3QAHRR6R4IELSQJ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RPIWTQ4CDWL3QAHRR6R4IELSQJ/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-09T08:52:56Z","links":{"resolver":"https://pith.science/pith/RPIWTQ4CDWL3QAHRR6R4IELSQJ","bundle":"https://pith.science/pith/RPIWTQ4CDWL3QAHRR6R4IELSQJ/bundle.json","state":"https://pith.science/pith/RPIWTQ4CDWL3QAHRR6R4IELSQJ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RPIWTQ4CDWL3QAHRR6R4IELSQJ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:RPIWTQ4CDWL3QAHRR6R4IELSQJ","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":"c5d06d5fb78cc12c20ea7e816cb029202d92b53748b5a0ec4fb50578c1202efe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-30T00:35:06Z","title_canon_sha256":"838b337c3bea5ecb759522a21950f6fb1d5e04df68f2f535a1010101a277777d"},"schema_version":"1.0","source":{"id":"1804.11008","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1804.11008","created_at":"2026-05-18T00:04:07Z"},{"alias_kind":"arxiv_version","alias_value":"1804.11008v2","created_at":"2026-05-18T00:04:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1804.11008","created_at":"2026-05-18T00:04:07Z"},{"alias_kind":"pith_short_12","alias_value":"RPIWTQ4CDWL3","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_16","alias_value":"RPIWTQ4CDWL3QAHR","created_at":"2026-05-18T12:32:50Z"},{"alias_kind":"pith_short_8","alias_value":"RPIWTQ4C","created_at":"2026-05-18T12:32:50Z"}],"graph_snapshots":[{"event_id":"sha256:3bf9f51cb48d3da65030c81901faf78744176dc88e1bbfc4081f9fecf79891c9","target":"graph","created_at":"2026-05-18T00:04:07Z","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":"We prove that for every graph $H$, there exists $\\varepsilon>0$ such that every $n$-vertex graph with no vertex-minors isomorphic to $H$ has a pair of disjoint sets $A$, $B$ of vertices such that $|A|, |B|\\ge \\varepsilon n$ and $A$ is complete or anticomplete to $B$. We deduce this from recent work of Chudnovsky, Scott, Seymour, and Spirkl (2018). This proves the analog of the Erd\\H{o}s-Hajnal conjecture for vertex-minors.","authors_text":"Maria Chudnovsky, Sang-il Oum","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-30T00:35:06Z","title":"Vertex-minors and the Erd\\H{o}s-Hajnal conjecture"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.11008","kind":"arxiv","version":2},"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":"sha256:286242179f11f549bf9c6e72756a7ec1c7fc6200b71cf61a08d445505c2bed1b","target":"record","created_at":"2026-05-18T00:04:07Z","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":"c5d06d5fb78cc12c20ea7e816cb029202d92b53748b5a0ec4fb50578c1202efe","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2018-04-30T00:35:06Z","title_canon_sha256":"838b337c3bea5ecb759522a21950f6fb1d5e04df68f2f535a1010101a277777d"},"schema_version":"1.0","source":{"id":"1804.11008","kind":"arxiv","version":2}},"canonical_sha256":"8bd169c3821d97b800f18fa3c4117282431049ee42f382b2879a060384a872c2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8bd169c3821d97b800f18fa3c4117282431049ee42f382b2879a060384a872c2","first_computed_at":"2026-05-18T00:04:07.736847Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:07.736847Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KoZSyghMcZppUIpWgTbCOcM2nNuQbv+D0UBK1Uy3NUJeerQitN6oKgiW5ti72my+S2QOhzW9RD4xQ7WZaSigCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:07.737542Z","signed_message":"canonical_sha256_bytes"},"source_id":"1804.11008","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:286242179f11f549bf9c6e72756a7ec1c7fc6200b71cf61a08d445505c2bed1b","sha256:3bf9f51cb48d3da65030c81901faf78744176dc88e1bbfc4081f9fecf79891c9"],"state_sha256":"718cce7e89211a6c81d9dc16d09b0c10855bb2f0ae02a9e7dc05162a6f1355a6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WJXDbSsBR0m7yogJusuLYEGl3M+5QJDDXyamQcJUUWRt1yroYTy/TeuM9AranQ1URwVYODChPAvqUCmUc8FzDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T08:52:56.877654Z","bundle_sha256":"9bf3fa714b60c4b18da2ea0bf44ea3ad057a22e882fcf927c6547f53e7f2db63"}}