{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:4TD5445PPAJ22ZGAWGRFWGE55Z","short_pith_number":"pith:4TD5445P","schema_version":"1.0","canonical_sha256":"e4c7de73af7813ad64c0b1a25b189dee4d23217cc02e24cceb94ca6c77135272","source":{"kind":"arxiv","id":"1306.1936","version":5},"attestation_state":"computed","paper":{"title":"On principles between $\\Sigma_1$- and $\\Sigma_2$-induction, and monotone enumerations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Alexander P. Kreuzer, Keita Yokoyama","submitted_at":"2013-06-08T15:51:13Z","abstract_excerpt":"We show that many principles of first-order arithmetic, previously only known to lie strictly between $\\Sigma_1$-induction and $\\Sigma_2$-induction, are equivalent to the well-foundedness of $\\omega^\\omega$.\n  Among these principles are the iteration of partial functions ($P\\Sigma_1$) of H\\'ajek and Paris, the bounded monotone enumerations principle (non-iterated, BME$_1$) by Chong, Slaman, and Yang, the relativized Paris-Harrington principle for pairs, and the totality of the relativized Ackermann-P\\'eter function.\n  With this we show that the well-foundedness of $\\omega^\\omega$ is a far more"},"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":"1306.1936","kind":"arxiv","version":5},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-06-08T15:51:13Z","cross_cats_sorted":[],"title_canon_sha256":"d7c476e81643e19f347b4398c38e257662cb9358f698e92d1a685acbda8d0332","abstract_canon_sha256":"42762ac4310816245d6eb0daebf20830a824a8831328e6f07cbc4380368864fa"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:24:30.920957Z","signature_b64":"d2DrSTJrVDjaXrDdjU6DOdKvhPNbuDRjOQRn/M3UdX6QPLQccJM6mfimkJCHeb9AmRvGLhWytfezi5+x4w4iBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e4c7de73af7813ad64c0b1a25b189dee4d23217cc02e24cceb94ca6c77135272","last_reissued_at":"2026-05-18T01:24:30.920521Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:24:30.920521Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On principles between $\\Sigma_1$- and $\\Sigma_2$-induction, and monotone enumerations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Alexander P. Kreuzer, Keita Yokoyama","submitted_at":"2013-06-08T15:51:13Z","abstract_excerpt":"We show that many principles of first-order arithmetic, previously only known to lie strictly between $\\Sigma_1$-induction and $\\Sigma_2$-induction, are equivalent to the well-foundedness of $\\omega^\\omega$.\n  Among these principles are the iteration of partial functions ($P\\Sigma_1$) of H\\'ajek and Paris, the bounded monotone enumerations principle (non-iterated, BME$_1$) by Chong, Slaman, and Yang, the relativized Paris-Harrington principle for pairs, and the totality of the relativized Ackermann-P\\'eter function.\n  With this we show that the well-foundedness of $\\omega^\\omega$ is a far more"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.1936","kind":"arxiv","version":5},"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":"1306.1936","created_at":"2026-05-18T01:24:30.920583+00:00"},{"alias_kind":"arxiv_version","alias_value":"1306.1936v5","created_at":"2026-05-18T01:24:30.920583+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.1936","created_at":"2026-05-18T01:24:30.920583+00:00"},{"alias_kind":"pith_short_12","alias_value":"4TD5445PPAJ2","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_16","alias_value":"4TD5445PPAJ22ZGA","created_at":"2026-05-18T12:27:34.582898+00:00"},{"alias_kind":"pith_short_8","alias_value":"4TD5445P","created_at":"2026-05-18T12:27:34.582898+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/4TD5445PPAJ22ZGAWGRFWGE55Z","json":"https://pith.science/pith/4TD5445PPAJ22ZGAWGRFWGE55Z.json","graph_json":"https://pith.science/api/pith-number/4TD5445PPAJ22ZGAWGRFWGE55Z/graph.json","events_json":"https://pith.science/api/pith-number/4TD5445PPAJ22ZGAWGRFWGE55Z/events.json","paper":"https://pith.science/paper/4TD5445P"},"agent_actions":{"view_html":"https://pith.science/pith/4TD5445PPAJ22ZGAWGRFWGE55Z","download_json":"https://pith.science/pith/4TD5445PPAJ22ZGAWGRFWGE55Z.json","view_paper":"https://pith.science/paper/4TD5445P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1306.1936&json=true","fetch_graph":"https://pith.science/api/pith-number/4TD5445PPAJ22ZGAWGRFWGE55Z/graph.json","fetch_events":"https://pith.science/api/pith-number/4TD5445PPAJ22ZGAWGRFWGE55Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4TD5445PPAJ22ZGAWGRFWGE55Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4TD5445PPAJ22ZGAWGRFWGE55Z/action/storage_attestation","attest_author":"https://pith.science/pith/4TD5445PPAJ22ZGAWGRFWGE55Z/action/author_attestation","sign_citation":"https://pith.science/pith/4TD5445PPAJ22ZGAWGRFWGE55Z/action/citation_signature","submit_replication":"https://pith.science/pith/4TD5445PPAJ22ZGAWGRFWGE55Z/action/replication_record"}},"created_at":"2026-05-18T01:24:30.920583+00:00","updated_at":"2026-05-18T01:24:30.920583+00:00"}