{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2026:47BAZ2UJCNHVBC2UC5FDFGVDLK","short_pith_number":"pith:47BAZ2UJ","schema_version":"1.0","canonical_sha256":"e7c20cea89134f508b54174a329aa35a9c05ff05fb7632a430aceb11a2773e7e","source":{"kind":"arxiv","id":"2605.13944","version":1},"attestation_state":"computed","paper":{"title":"A foundational characterization of Hoare Logic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A partial-correctness assertion for an iterative program is provable in Hoare logic if and only if it is provable in second-order logic with first-order comprehension.","cross_cats":["math.LO"],"primary_cat":"cs.LO","authors_text":"Daniel Leivant","submitted_at":"2026-05-13T17:51:13Z","abstract_excerpt":"We show that a partial-correctness assertion about an iterative program is provable in Hoare Logic iffit is provable in standard second-order logic with comprehension restricted to first-order predicates. This equivalence was claimed twice in the past, both with faulty proofs, and seems to be the first foundational characterization of Hoare Logic."},"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":true,"formal_links_present":true},"canonical_record":{"source":{"id":"2605.13944","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2026-05-13T17:51:13Z","cross_cats_sorted":["math.LO"],"title_canon_sha256":"4f040d277ff0466df169b64e0999ca093eae132788f3fb01990a048a68c7d613","abstract_canon_sha256":"5f5f9129f7e6f98837f40572a283aecbf95bab1ba1c1654c33ff1488f90b3b6a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:39:13.822113Z","signature_b64":"Be9Hw94K4jZlr1+27XmbNMyo+ApT97O90gwYztoTkTIzmOGMM7nPtVuaMJtoj8hIxd81WFvpREkxrauS6YlyDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7c20cea89134f508b54174a329aa35a9c05ff05fb7632a430aceb11a2773e7e","last_reissued_at":"2026-05-17T23:39:13.821427Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:39:13.821427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A foundational characterization of Hoare Logic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"A partial-correctness assertion for an iterative program is provable in Hoare logic if and only if it is provable in second-order logic with first-order comprehension.","cross_cats":["math.LO"],"primary_cat":"cs.LO","authors_text":"Daniel Leivant","submitted_at":"2026-05-13T17:51:13Z","abstract_excerpt":"We show that a partial-correctness assertion about an iterative program is provable in Hoare Logic iffit is provable in standard second-order logic with comprehension restricted to first-order predicates. This equivalence was claimed twice in the past, both with faulty proofs, and seems to be the first foundational characterization of Hoare Logic."},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"a partial-correctness assertion about an iterative program is provable in Hoare Logic iff it is provable in standard second-order logic with comprehension restricted to first-order predicates.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The equivalence depends on the precise syntactic definitions of Hoare logic for iterative programs and on the exact restriction of comprehension to first-order predicates; any deviation in these definitions would invalidate the claimed if-and-only-if.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"Partial-correctness assertions for iterative programs are provable in Hoare logic if and only if they are provable in second-order logic with comprehension restricted to first-order predicates.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"A partial-correctness assertion for an iterative program is provable in Hoare logic if and only if it is provable in second-order logic with first-order comprehension.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"f8b8b95a3f86985cd91af61bb7ec6a69306f1c3314b49883aa9e77d87b080917"},"source":{"id":"2605.13944","kind":"arxiv","version":1},"verdict":{"id":"333e2f73-08d5-4c69-9fb5-09c2859dc221","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-15T02:40:04.722172Z","strongest_claim":"a partial-correctness assertion about an iterative program is provable in Hoare Logic iff it is provable in standard second-order logic with comprehension restricted to first-order predicates.","one_line_summary":"Partial-correctness assertions for iterative programs are provable in Hoare logic if and only if they are provable in second-order logic with comprehension restricted to first-order predicates.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The equivalence depends on the precise syntactic definitions of Hoare logic for iterative programs and on the exact restriction of comprehension to first-order predicates; any deviation in these definitions would invalidate the claimed if-and-only-if.","pith_extraction_headline":"A partial-correctness assertion for an iterative program is provable in Hoare logic if and only if it is provable in second-order logic with first-order comprehension."},"references":{"count":216,"sample":[{"doi":"","year":null,"title":"Stephen Simpson , title=","work_id":"32922cba-c5ba-4574-ba32-f086f91d1260","ref_index":1,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Dynamic Logic","work_id":"d1b04a75-ee0a-4c7a-9f41-df293f3d4d53","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Arithmetices principia, novo methodo exposita","work_id":"8ddfcebb-6139-4a23-84e4-cd245e902779","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":1931,"title":"van Heijenoort","work_id":"62044c68-d023-4fd4-a37e-c44d97e8fa21","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":null,"title":"Ramified recurrence and computational complexity I : Word recurrence and poly-time","work_id":"28fdb9a5-5620-4806-ad21-9d2f07475645","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":216,"snapshot_sha256":"d31674114d4b670adbbbee16a244b35e2afe7b61fac5235f0f18cde26f41fbbc","internal_anchors":0},"formal_canon":{"evidence_count":2,"snapshot_sha256":"9fc7cfa8567581c8579cfc969c4d12bcee38cb2177ed73c6ffd95779e0313518"},"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":"2605.13944","created_at":"2026-05-17T23:39:13.821533+00:00"},{"alias_kind":"arxiv_version","alias_value":"2605.13944v1","created_at":"2026-05-17T23:39:13.821533+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2605.13944","created_at":"2026-05-17T23:39:13.821533+00:00"},{"alias_kind":"pith_short_12","alias_value":"47BAZ2UJCNHV","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_16","alias_value":"47BAZ2UJCNHVBC2U","created_at":"2026-05-18T12:33:37.589309+00:00"},{"alias_kind":"pith_short_8","alias_value":"47BAZ2UJ","created_at":"2026-05-18T12:33:37.589309+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":2,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/47BAZ2UJCNHVBC2UC5FDFGVDLK","json":"https://pith.science/pith/47BAZ2UJCNHVBC2UC5FDFGVDLK.json","graph_json":"https://pith.science/api/pith-number/47BAZ2UJCNHVBC2UC5FDFGVDLK/graph.json","events_json":"https://pith.science/api/pith-number/47BAZ2UJCNHVBC2UC5FDFGVDLK/events.json","paper":"https://pith.science/paper/47BAZ2UJ"},"agent_actions":{"view_html":"https://pith.science/pith/47BAZ2UJCNHVBC2UC5FDFGVDLK","download_json":"https://pith.science/pith/47BAZ2UJCNHVBC2UC5FDFGVDLK.json","view_paper":"https://pith.science/paper/47BAZ2UJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2605.13944&json=true","fetch_graph":"https://pith.science/api/pith-number/47BAZ2UJCNHVBC2UC5FDFGVDLK/graph.json","fetch_events":"https://pith.science/api/pith-number/47BAZ2UJCNHVBC2UC5FDFGVDLK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/47BAZ2UJCNHVBC2UC5FDFGVDLK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/47BAZ2UJCNHVBC2UC5FDFGVDLK/action/storage_attestation","attest_author":"https://pith.science/pith/47BAZ2UJCNHVBC2UC5FDFGVDLK/action/author_attestation","sign_citation":"https://pith.science/pith/47BAZ2UJCNHVBC2UC5FDFGVDLK/action/citation_signature","submit_replication":"https://pith.science/pith/47BAZ2UJCNHVBC2UC5FDFGVDLK/action/replication_record"}},"created_at":"2026-05-17T23:39:13.821533+00:00","updated_at":"2026-05-17T23:39:13.821533+00:00"}