{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:LMVLK44JOAFGR52UFVLMR6DUIV","short_pith_number":"pith:LMVLK44J","schema_version":"1.0","canonical_sha256":"5b2ab57389700a68f7542d56c8f87445419129a81e2ad1245f1dfb4e924c6f64","source":{"kind":"arxiv","id":"1810.01513","version":4},"attestation_state":"computed","paper":{"title":"Erd\\H{o}s-Rado Classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Will Boney","submitted_at":"2018-10-02T21:07:27Z","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."},"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":"1810.01513","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-10-02T21:07:27Z","cross_cats_sorted":[],"title_canon_sha256":"26b658a882a6752b207e0b875366c5482854110c8dccde7594f334211dc047fe","abstract_canon_sha256":"713a62026b340d8f19ea03dfa1fca8bd9f177fe21978e047868e0cee0bc14403"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-12T00:07:47.869754Z","signature_b64":"DXcN4LEINHJigdnF9mbnQt+smiGfdmL2D672deqbk1iQ7DICRQqyKPF5Af4pGUUVm9tBBd8Z6/H4OjJgL8T1Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5b2ab57389700a68f7542d56c8f87445419129a81e2ad1245f1dfb4e924c6f64","last_reissued_at":"2026-06-12T00:07:47.868191Z","signature_status":"signed_v1","first_computed_at":"2026-06-12T00:07:47.868191Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Erd\\H{o}s-Rado Classes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Will Boney","submitted_at":"2018-10-02T21:07:27Z","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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.01513","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1810.01513/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1810.01513","created_at":"2026-06-12T00:07:47.868263+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.01513v4","created_at":"2026-06-12T00:07:47.868263+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.01513","created_at":"2026-06-12T00:07:47.868263+00:00"},{"alias_kind":"pith_short_12","alias_value":"LMVLK44JOAFG","created_at":"2026-06-12T00:07:47.868263+00:00"},{"alias_kind":"pith_short_16","alias_value":"LMVLK44JOAFGR52U","created_at":"2026-06-12T00:07:47.868263+00:00"},{"alias_kind":"pith_short_8","alias_value":"LMVLK44J","created_at":"2026-06-12T00:07:47.868263+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/LMVLK44JOAFGR52UFVLMR6DUIV","json":"https://pith.science/pith/LMVLK44JOAFGR52UFVLMR6DUIV.json","graph_json":"https://pith.science/api/pith-number/LMVLK44JOAFGR52UFVLMR6DUIV/graph.json","events_json":"https://pith.science/api/pith-number/LMVLK44JOAFGR52UFVLMR6DUIV/events.json","paper":"https://pith.science/paper/LMVLK44J"},"agent_actions":{"view_html":"https://pith.science/pith/LMVLK44JOAFGR52UFVLMR6DUIV","download_json":"https://pith.science/pith/LMVLK44JOAFGR52UFVLMR6DUIV.json","view_paper":"https://pith.science/paper/LMVLK44J","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.01513&json=true","fetch_graph":"https://pith.science/api/pith-number/LMVLK44JOAFGR52UFVLMR6DUIV/graph.json","fetch_events":"https://pith.science/api/pith-number/LMVLK44JOAFGR52UFVLMR6DUIV/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/LMVLK44JOAFGR52UFVLMR6DUIV/action/timestamp_anchor","attest_storage":"https://pith.science/pith/LMVLK44JOAFGR52UFVLMR6DUIV/action/storage_attestation","attest_author":"https://pith.science/pith/LMVLK44JOAFGR52UFVLMR6DUIV/action/author_attestation","sign_citation":"https://pith.science/pith/LMVLK44JOAFGR52UFVLMR6DUIV/action/citation_signature","submit_replication":"https://pith.science/pith/LMVLK44JOAFGR52UFVLMR6DUIV/action/replication_record"}},"created_at":"2026-06-12T00:07:47.868263+00:00","updated_at":"2026-06-12T00:07:47.868263+00:00"}