{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:HQSIZOCCSVSCCXWWHNNRZ4WUPI","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":"c91312898a8ceaa33971d6f19c331c182c20be80629f9deac5aed275d1b46c97","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-11-16T12:19:41Z","title_canon_sha256":"799cc213dc8793024a9ccacc3548a613b8a2a368eeb7aa11f11c2b7a38aa43bf"},"schema_version":"1.0","source":{"id":"1211.3876","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.3876","created_at":"2026-05-18T00:37:53Z"},{"alias_kind":"arxiv_version","alias_value":"1211.3876v3","created_at":"2026-05-18T00:37:53Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.3876","created_at":"2026-05-18T00:37:53Z"},{"alias_kind":"pith_short_12","alias_value":"HQSIZOCCSVSC","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_16","alias_value":"HQSIZOCCSVSCCXWW","created_at":"2026-05-18T12:27:09Z"},{"alias_kind":"pith_short_8","alias_value":"HQSIZOCC","created_at":"2026-05-18T12:27:09Z"}],"graph_snapshots":[{"event_id":"sha256:ff65f7bc2e13c21f7e363249f77b9125a504bb4deb972417942d46d0bf356c6a","target":"graph","created_at":"2026-05-18T00:37:53Z","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":"In their celebrated paper [Ramsey-Type Theorems, Discrete Appl. Math. 25 (1989) 37-52], Erd\\H{o}s and Hajnal asked the following: is it true, that for any finite graph H there exists a constant c(H) such that for any finite graph G, if G does not contain complete or empty induced subgraphs of size at least |V(G)|^c(H), then H can be isomorphically embedded into G ? The positive answer has become known as the Erd\\H{o}s-Hajnal conjecture.\n  In Theorem 3.20 of the present paper we settle this conjecture in the affirmative. To do so, we are studying here the fine structure of ultraproducts of fini","authors_text":"G\\'abor S\\'agi","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-11-16T12:19:41Z","title":"On Induced Subgraphs of Finite Graphs not Containing Large Empty and Complete Subgraphs"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3876","kind":"arxiv","version":3},"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":"sha256:4118d8f08a874cb85b7d12b32aea43f63ec574a3580c0f74f26b0f88f15241e3","target":"record","created_at":"2026-05-18T00:37:53Z","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":"c91312898a8ceaa33971d6f19c331c182c20be80629f9deac5aed275d1b46c97","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-11-16T12:19:41Z","title_canon_sha256":"799cc213dc8793024a9ccacc3548a613b8a2a368eeb7aa11f11c2b7a38aa43bf"},"schema_version":"1.0","source":{"id":"1211.3876","kind":"arxiv","version":3}},"canonical_sha256":"3c248cb8429564215ed63b5b1cf2d47a3c082fd8fbe90cd6e5e7ca0179010015","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"3c248cb8429564215ed63b5b1cf2d47a3c082fd8fbe90cd6e5e7ca0179010015","first_computed_at":"2026-05-18T00:37:53.070523Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:37:53.070523Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/NtomipPxCaSCDA6Jin/cSl4CYTNE708nGWVm2El0aFHfn7OmUwPPaVMQfIyIhpB4+rTmAUzT3BO73s/RiVaAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:37:53.070983Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.3876","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:4118d8f08a874cb85b7d12b32aea43f63ec574a3580c0f74f26b0f88f15241e3","sha256:ff65f7bc2e13c21f7e363249f77b9125a504bb4deb972417942d46d0bf356c6a"],"state_sha256":"140e23bf82a676f01a357cc456fa0136ccc672fac3a4437db9a7456b2b2e18c8"}