{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:DLXZHG2PG25OFJD2P2HX5JLBPZ","short_pith_number":"pith:DLXZHG2P","schema_version":"1.0","canonical_sha256":"1aef939b4f36bae2a47a7e8f7ea5617e66d685d3dcda781f7f9cfa0c7f92c781","source":{"kind":"arxiv","id":"1810.09072","version":1},"attestation_state":"computed","paper":{"title":"On $\\left( 1,\\omega_{1}\\right) $\\emph{-}weakly universal functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Osvaldo Guzman","submitted_at":"2018-10-22T03:36:47Z","abstract_excerpt":"A function $U:\\left[ \\omega_{1}\\right] ^{2}\\longrightarrow\\omega$ is called $\\left( 1,\\omega_{1}\\right) $\\emph{-weakly universal }if for every function $F:\\left[ \\omega_{1}\\right] ^{2}\\longrightarrow\\omega$ there is an injective function $h:\\omega_{1}\\longrightarrow\\omega_{1}$ and a function $e:\\omega \\longrightarrow\\omega$ such that $F\\left( \\alpha,\\beta\\right) =e\\left( U\\left( h\\left( \\alpha\\right) ,h\\left( \\beta\\right) \\right) \\right) $ for every $\\alpha,\\beta\\in\\omega_{1}$. We will prove that it is consistent that there are no $\\left( 1,\\omega_{1}\\right) $\\emph{-}weakly universal functions"},"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":"1810.09072","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-10-22T03:36:47Z","cross_cats_sorted":[],"title_canon_sha256":"ad5b55f59646d2b159770e2431972d04d78998740a972250bb5e6106e13b854a","abstract_canon_sha256":"e8116bdb3097a83efc473c1e6f2328a09068384e824b571e122d4caf8362b16e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:02:41.092391Z","signature_b64":"MRKGiGUr3O2DhZzbzMxgb5le077cnq9moen5ItQS8oyms7vm9sbpN6EWKF7VvVuXa5Cln5JQG+K6lz6zSRNKCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1aef939b4f36bae2a47a7e8f7ea5617e66d685d3dcda781f7f9cfa0c7f92c781","last_reissued_at":"2026-05-18T00:02:41.091927Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:02:41.091927Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On $\\left( 1,\\omega_{1}\\right) $\\emph{-}weakly universal functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Osvaldo Guzman","submitted_at":"2018-10-22T03:36:47Z","abstract_excerpt":"A function $U:\\left[ \\omega_{1}\\right] ^{2}\\longrightarrow\\omega$ is called $\\left( 1,\\omega_{1}\\right) $\\emph{-weakly universal }if for every function $F:\\left[ \\omega_{1}\\right] ^{2}\\longrightarrow\\omega$ there is an injective function $h:\\omega_{1}\\longrightarrow\\omega_{1}$ and a function $e:\\omega \\longrightarrow\\omega$ such that $F\\left( \\alpha,\\beta\\right) =e\\left( U\\left( h\\left( \\alpha\\right) ,h\\left( \\beta\\right) \\right) \\right) $ for every $\\alpha,\\beta\\in\\omega_{1}$. We will prove that it is consistent that there are no $\\left( 1,\\omega_{1}\\right) $\\emph{-}weakly universal functions"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.09072","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1810.09072","created_at":"2026-05-18T00:02:41.091989+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.09072v1","created_at":"2026-05-18T00:02:41.091989+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.09072","created_at":"2026-05-18T00:02:41.091989+00:00"},{"alias_kind":"pith_short_12","alias_value":"DLXZHG2PG25O","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_16","alias_value":"DLXZHG2PG25OFJD2","created_at":"2026-05-18T12:32:19.392346+00:00"},{"alias_kind":"pith_short_8","alias_value":"DLXZHG2P","created_at":"2026-05-18T12:32:19.392346+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/DLXZHG2PG25OFJD2P2HX5JLBPZ","json":"https://pith.science/pith/DLXZHG2PG25OFJD2P2HX5JLBPZ.json","graph_json":"https://pith.science/api/pith-number/DLXZHG2PG25OFJD2P2HX5JLBPZ/graph.json","events_json":"https://pith.science/api/pith-number/DLXZHG2PG25OFJD2P2HX5JLBPZ/events.json","paper":"https://pith.science/paper/DLXZHG2P"},"agent_actions":{"view_html":"https://pith.science/pith/DLXZHG2PG25OFJD2P2HX5JLBPZ","download_json":"https://pith.science/pith/DLXZHG2PG25OFJD2P2HX5JLBPZ.json","view_paper":"https://pith.science/paper/DLXZHG2P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.09072&json=true","fetch_graph":"https://pith.science/api/pith-number/DLXZHG2PG25OFJD2P2HX5JLBPZ/graph.json","fetch_events":"https://pith.science/api/pith-number/DLXZHG2PG25OFJD2P2HX5JLBPZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DLXZHG2PG25OFJD2P2HX5JLBPZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DLXZHG2PG25OFJD2P2HX5JLBPZ/action/storage_attestation","attest_author":"https://pith.science/pith/DLXZHG2PG25OFJD2P2HX5JLBPZ/action/author_attestation","sign_citation":"https://pith.science/pith/DLXZHG2PG25OFJD2P2HX5JLBPZ/action/citation_signature","submit_replication":"https://pith.science/pith/DLXZHG2PG25OFJD2P2HX5JLBPZ/action/replication_record"}},"created_at":"2026-05-18T00:02:41.091989+00:00","updated_at":"2026-05-18T00:02:41.091989+00:00"}