{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:XMGRTYRT5POHY3W34OA4A2NPDI","short_pith_number":"pith:XMGRTYRT","schema_version":"1.0","canonical_sha256":"bb0d19e233ebdc7c6edbe381c069af1a35403381e4d678b3b378589b5f3efa30","source":{"kind":"arxiv","id":"1410.2537","version":2},"attestation_state":"computed","paper":{"title":"Counterexamples to countable-section $\\varPi^1_2$ uniformization and $\\varPi^1_3$ separation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Vassily Lyubetsky, Vladimir Kanovei","submitted_at":"2014-10-09T17:27:12Z","abstract_excerpt":"We make use of a finite support product of the Jensen minimal $\\varPi^1_2$ singleton forcing to define a model in which $\\varPi^1_2$ Uniformization fails for a set with countable cross-sections. We also define appropriate submodels of the same model in which Separation fails for $\\varPi^1_3$."},"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":"1410.2537","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2014-10-09T17:27:12Z","cross_cats_sorted":[],"title_canon_sha256":"447ad724cd2da2a84ff70d945aca67e2c4a366533d48fc540ec16d6bd190a7b3","abstract_canon_sha256":"1c399bd53760cff4952f58c5b0a29334b4233aef103530d71da85d856092d814"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:08:05.510335Z","signature_b64":"ofI5akzi8gun6DK6nbaTMmcApI7TVGlUvTIcDqhS+JDdYeLX0sV9G3AwcNVI7i5dIuL1YKwqcOQLEO1lzxd9AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bb0d19e233ebdc7c6edbe381c069af1a35403381e4d678b3b378589b5f3efa30","last_reissued_at":"2026-05-18T00:08:05.509874Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:08:05.509874Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Counterexamples to countable-section $\\varPi^1_2$ uniformization and $\\varPi^1_3$ separation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Vassily Lyubetsky, Vladimir Kanovei","submitted_at":"2014-10-09T17:27:12Z","abstract_excerpt":"We make use of a finite support product of the Jensen minimal $\\varPi^1_2$ singleton forcing to define a model in which $\\varPi^1_2$ Uniformization fails for a set with countable cross-sections. We also define appropriate submodels of the same model in which Separation fails for $\\varPi^1_3$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.2537","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1410.2537","created_at":"2026-05-18T00:08:05.509939+00:00"},{"alias_kind":"arxiv_version","alias_value":"1410.2537v2","created_at":"2026-05-18T00:08:05.509939+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1410.2537","created_at":"2026-05-18T00:08:05.509939+00:00"},{"alias_kind":"pith_short_12","alias_value":"XMGRTYRT5POH","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_16","alias_value":"XMGRTYRT5POHY3W3","created_at":"2026-05-18T12:28:57.508820+00:00"},{"alias_kind":"pith_short_8","alias_value":"XMGRTYRT","created_at":"2026-05-18T12:28:57.508820+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/XMGRTYRT5POHY3W34OA4A2NPDI","json":"https://pith.science/pith/XMGRTYRT5POHY3W34OA4A2NPDI.json","graph_json":"https://pith.science/api/pith-number/XMGRTYRT5POHY3W34OA4A2NPDI/graph.json","events_json":"https://pith.science/api/pith-number/XMGRTYRT5POHY3W34OA4A2NPDI/events.json","paper":"https://pith.science/paper/XMGRTYRT"},"agent_actions":{"view_html":"https://pith.science/pith/XMGRTYRT5POHY3W34OA4A2NPDI","download_json":"https://pith.science/pith/XMGRTYRT5POHY3W34OA4A2NPDI.json","view_paper":"https://pith.science/paper/XMGRTYRT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1410.2537&json=true","fetch_graph":"https://pith.science/api/pith-number/XMGRTYRT5POHY3W34OA4A2NPDI/graph.json","fetch_events":"https://pith.science/api/pith-number/XMGRTYRT5POHY3W34OA4A2NPDI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XMGRTYRT5POHY3W34OA4A2NPDI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XMGRTYRT5POHY3W34OA4A2NPDI/action/storage_attestation","attest_author":"https://pith.science/pith/XMGRTYRT5POHY3W34OA4A2NPDI/action/author_attestation","sign_citation":"https://pith.science/pith/XMGRTYRT5POHY3W34OA4A2NPDI/action/citation_signature","submit_replication":"https://pith.science/pith/XMGRTYRT5POHY3W34OA4A2NPDI/action/replication_record"}},"created_at":"2026-05-18T00:08:05.509939+00:00","updated_at":"2026-05-18T00:08:05.509939+00:00"}