{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:FW6OQSJPY5XPWBCPHY3E2BLGVE","short_pith_number":"pith:FW6OQSJP","schema_version":"1.0","canonical_sha256":"2dbce8492fc76efb044f3e364d0566a916a7b70f3cec0ebb8eb988fefaec76c8","source":{"kind":"arxiv","id":"1811.09964","version":7},"attestation_state":"computed","paper":{"title":"Proof-theoretic strengths of the well ordering principles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Toshiyasu Arai","submitted_at":"2018-11-25T06:45:17Z","abstract_excerpt":"In this note the proof-theoretic ordinal of the well-ordering principle for the normal functions ${\\sf g}$ on ordinals is shown to be equal to the least fixed point of ${\\sf g}$. Moreover corrections to the previous paper are made."},"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":"1811.09964","kind":"arxiv","version":7},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2018-11-25T06:45:17Z","cross_cats_sorted":[],"title_canon_sha256":"779cd89a15ea43224cb55c4341d9ebb7fcf08d09a7a384a3d1f944792eec24d7","abstract_canon_sha256":"dd195df81a8125150f6947664660fcea53152d726eafd1893395fa56accea639"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:45:46.555783Z","signature_b64":"M0b2nCm0zXReF2wn7xTTb5GJ3ESLILueNRSe7FOj/4ipCNb7q1TK02zuIxvVDOUXQOH5eY61LcV3z0dJteXSAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2dbce8492fc76efb044f3e364d0566a916a7b70f3cec0ebb8eb988fefaec76c8","last_reissued_at":"2026-05-17T23:45:46.555369Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:45:46.555369Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Proof-theoretic strengths of the well ordering principles","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Toshiyasu Arai","submitted_at":"2018-11-25T06:45:17Z","abstract_excerpt":"In this note the proof-theoretic ordinal of the well-ordering principle for the normal functions ${\\sf g}$ on ordinals is shown to be equal to the least fixed point of ${\\sf g}$. Moreover corrections to the previous paper are made."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.09964","kind":"arxiv","version":7},"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":"1811.09964","created_at":"2026-05-17T23:45:46.555438+00:00"},{"alias_kind":"arxiv_version","alias_value":"1811.09964v7","created_at":"2026-05-17T23:45:46.555438+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.09964","created_at":"2026-05-17T23:45:46.555438+00:00"},{"alias_kind":"pith_short_12","alias_value":"FW6OQSJPY5XP","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_16","alias_value":"FW6OQSJPY5XPWBCP","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_8","alias_value":"FW6OQSJP","created_at":"2026-05-18T12:32:25.280505+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/FW6OQSJPY5XPWBCPHY3E2BLGVE","json":"https://pith.science/pith/FW6OQSJPY5XPWBCPHY3E2BLGVE.json","graph_json":"https://pith.science/api/pith-number/FW6OQSJPY5XPWBCPHY3E2BLGVE/graph.json","events_json":"https://pith.science/api/pith-number/FW6OQSJPY5XPWBCPHY3E2BLGVE/events.json","paper":"https://pith.science/paper/FW6OQSJP"},"agent_actions":{"view_html":"https://pith.science/pith/FW6OQSJPY5XPWBCPHY3E2BLGVE","download_json":"https://pith.science/pith/FW6OQSJPY5XPWBCPHY3E2BLGVE.json","view_paper":"https://pith.science/paper/FW6OQSJP","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1811.09964&json=true","fetch_graph":"https://pith.science/api/pith-number/FW6OQSJPY5XPWBCPHY3E2BLGVE/graph.json","fetch_events":"https://pith.science/api/pith-number/FW6OQSJPY5XPWBCPHY3E2BLGVE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FW6OQSJPY5XPWBCPHY3E2BLGVE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FW6OQSJPY5XPWBCPHY3E2BLGVE/action/storage_attestation","attest_author":"https://pith.science/pith/FW6OQSJPY5XPWBCPHY3E2BLGVE/action/author_attestation","sign_citation":"https://pith.science/pith/FW6OQSJPY5XPWBCPHY3E2BLGVE/action/citation_signature","submit_replication":"https://pith.science/pith/FW6OQSJPY5XPWBCPHY3E2BLGVE/action/replication_record"}},"created_at":"2026-05-17T23:45:46.555438+00:00","updated_at":"2026-05-17T23:45:46.555438+00:00"}