{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:UHGY6PD23T4PMXZWBZFD22CR5Z","short_pith_number":"pith:UHGY6PD2","schema_version":"1.0","canonical_sha256":"a1cd8f3c7adcf8f65f360e4a3d6851ee60bc7a0a4420468bbb8efafacfe63ada","source":{"kind":"arxiv","id":"2606.22584","version":1},"attestation_state":"computed","paper":{"title":"Second order logic and Set Theory Redux","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Jouko V\\\"a\\\"an\\\"anen","submitted_at":"2026-06-21T16:42:22Z","abstract_excerpt":"We argue that second order logic is a weaker form of set theory, despite the fact that the former is formalized in a second order langauge and the latter in a first order language. Along the way, we review the history of interactions between second order logic and set theory, as well as some modern trends."},"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":"2606.22584","kind":"arxiv","version":1},"metadata":{"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.LO","submitted_at":"2026-06-21T16:42:22Z","cross_cats_sorted":[],"title_canon_sha256":"2b8ba5913f06b1e562d830219e6e6d6011f4b70fe66242bb35995c9e815b56d0","abstract_canon_sha256":"97f4a0d66a0ac81de5341d5d46518eecdcb415f5718961c28831401e147a25a3"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-23T02:13:42.198656Z","signature_b64":"z6sAsNB2CKgWhcX/CXs+KC0uN+9d2LP5TypE2weh1Nsm27SoM2GvzJGCCD02jD1zHc3hZnkSJ0CwhrNGRfa4Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a1cd8f3c7adcf8f65f360e4a3d6851ee60bc7a0a4420468bbb8efafacfe63ada","last_reissued_at":"2026-06-23T02:13:42.198278Z","signature_status":"signed_v1","first_computed_at":"2026-06-23T02:13:42.198278Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Second order logic and Set Theory Redux","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Jouko V\\\"a\\\"an\\\"anen","submitted_at":"2026-06-21T16:42:22Z","abstract_excerpt":"We argue that second order logic is a weaker form of set theory, despite the fact that the former is formalized in a second order langauge and the latter in a first order language. Along the way, we review the history of interactions between second order logic and set theory, as well as some modern trends."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.22584","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.22584/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":"2606.22584","created_at":"2026-06-23T02:13:42.198344+00:00"},{"alias_kind":"arxiv_version","alias_value":"2606.22584v1","created_at":"2026-06-23T02:13:42.198344+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2606.22584","created_at":"2026-06-23T02:13:42.198344+00:00"},{"alias_kind":"pith_short_12","alias_value":"UHGY6PD23T4P","created_at":"2026-06-23T02:13:42.198344+00:00"},{"alias_kind":"pith_short_16","alias_value":"UHGY6PD23T4PMXZW","created_at":"2026-06-23T02:13:42.198344+00:00"},{"alias_kind":"pith_short_8","alias_value":"UHGY6PD2","created_at":"2026-06-23T02:13:42.198344+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/UHGY6PD23T4PMXZWBZFD22CR5Z","json":"https://pith.science/pith/UHGY6PD23T4PMXZWBZFD22CR5Z.json","graph_json":"https://pith.science/api/pith-number/UHGY6PD23T4PMXZWBZFD22CR5Z/graph.json","events_json":"https://pith.science/api/pith-number/UHGY6PD23T4PMXZWBZFD22CR5Z/events.json","paper":"https://pith.science/paper/UHGY6PD2"},"agent_actions":{"view_html":"https://pith.science/pith/UHGY6PD23T4PMXZWBZFD22CR5Z","download_json":"https://pith.science/pith/UHGY6PD23T4PMXZWBZFD22CR5Z.json","view_paper":"https://pith.science/paper/UHGY6PD2","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2606.22584&json=true","fetch_graph":"https://pith.science/api/pith-number/UHGY6PD23T4PMXZWBZFD22CR5Z/graph.json","fetch_events":"https://pith.science/api/pith-number/UHGY6PD23T4PMXZWBZFD22CR5Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UHGY6PD23T4PMXZWBZFD22CR5Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UHGY6PD23T4PMXZWBZFD22CR5Z/action/storage_attestation","attest_author":"https://pith.science/pith/UHGY6PD23T4PMXZWBZFD22CR5Z/action/author_attestation","sign_citation":"https://pith.science/pith/UHGY6PD23T4PMXZWBZFD22CR5Z/action/citation_signature","submit_replication":"https://pith.science/pith/UHGY6PD23T4PMXZWBZFD22CR5Z/action/replication_record"}},"created_at":"2026-06-23T02:13:42.198344+00:00","updated_at":"2026-06-23T02:13:42.198344+00:00"}