{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:LMVLK44JOAFGR52UFVLMR6DUIV","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":"713a62026b340d8f19ea03dfa1fca8bd9f177fe21978e047868e0cee0bc14403","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-10-02T21:07:27Z","title_canon_sha256":"26b658a882a6752b207e0b875366c5482854110c8dccde7594f334211dc047fe"},"schema_version":"1.0","source":{"id":"1810.01513","kind":"arxiv","version":4}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.01513","created_at":"2026-06-12T00:07:47Z"},{"alias_kind":"arxiv_version","alias_value":"1810.01513v4","created_at":"2026-06-12T00:07:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.01513","created_at":"2026-06-12T00:07:47Z"},{"alias_kind":"pith_short_12","alias_value":"LMVLK44JOAFG","created_at":"2026-06-12T00:07:47Z"},{"alias_kind":"pith_short_16","alias_value":"LMVLK44JOAFGR52U","created_at":"2026-06-12T00:07:47Z"},{"alias_kind":"pith_short_8","alias_value":"LMVLK44J","created_at":"2026-06-12T00:07:47Z"}],"graph_snapshots":[{"event_id":"sha256:aca39eda342caf3889fa208a7b93497865efd4918c772c4204037fb63d5dd025","target":"graph","created_at":"2026-06-12T00:07:47Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1810.01513/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We amalgamate two generalizations of Ramsey's Theorem--Ramsey classes and the Erd\\H{o}s-Rado Theorem--into the notion of a combinatorial Erd\\H{o}s-Rado class. These classes are closely related to Erd\\H{o}s-Rado classes, which are those from which we can build generalized indiscernibles and blueprints in nonelementary classes, especially Abstract Elementary Classes. We give several examples and some applications.","authors_text":"Will Boney","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-10-02T21:07:27Z","title":"Erd\\H{o}s-Rado Classes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.01513","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:a57c0a8e8baa814c0aec6903fd95a5e9ed7f0730f102c544cf9aed210276d583","target":"record","created_at":"2026-06-12T00:07:47Z","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":"713a62026b340d8f19ea03dfa1fca8bd9f177fe21978e047868e0cee0bc14403","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-10-02T21:07:27Z","title_canon_sha256":"26b658a882a6752b207e0b875366c5482854110c8dccde7594f334211dc047fe"},"schema_version":"1.0","source":{"id":"1810.01513","kind":"arxiv","version":4}},"canonical_sha256":"5b2ab57389700a68f7542d56c8f87445419129a81e2ad1245f1dfb4e924c6f64","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5b2ab57389700a68f7542d56c8f87445419129a81e2ad1245f1dfb4e924c6f64","first_computed_at":"2026-06-12T00:07:47.868191Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-06-12T00:07:47.868191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DXcN4LEINHJigdnF9mbnQt+smiGfdmL2D672deqbk1iQ7DICRQqyKPF5Af4pGUUVm9tBBd8Z6/H4OjJgL8T1Cw==","signature_status":"signed_v1","signed_at":"2026-06-12T00:07:47.869754Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.01513","source_kind":"arxiv","source_version":4}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a57c0a8e8baa814c0aec6903fd95a5e9ed7f0730f102c544cf9aed210276d583","sha256:aca39eda342caf3889fa208a7b93497865efd4918c772c4204037fb63d5dd025"],"state_sha256":"d521fd652429303e939ee1426463be670db16355a5eb57b0653d764d40c0fc9b"}