{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:SSV6WWJWIAH7IWN6PLFQIZBP7U","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"fee8a7ff4df6701f92e90c11478278fd1c533fb3bfd4da5c35bfa3c68218928a","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2018-10-19T07:37:46Z","title_canon_sha256":"6a85fa9dc48dbf8ee0693a6a74ca2a6b9a1a1158c80ac3458a7efc2f21349bf1"},"schema_version":"1.0","source":{"id":"1810.08380","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.08380","created_at":"2026-05-17T23:40:17Z"},{"alias_kind":"arxiv_version","alias_value":"1810.08380v3","created_at":"2026-05-17T23:40:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.08380","created_at":"2026-05-17T23:40:17Z"},{"alias_kind":"pith_short_12","alias_value":"SSV6WWJWIAH7","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_16","alias_value":"SSV6WWJWIAH7IWN6","created_at":"2026-05-18T12:32:53Z"},{"alias_kind":"pith_short_8","alias_value":"SSV6WWJW","created_at":"2026-05-18T12:32:53Z"}],"graph_snapshots":[{"event_id":"sha256:28e5742d37f33e7fa4023b5cfcc5d527a780d68411e01c043d4c1424419d903e","target":"graph","created_at":"2026-05-17T23:40:17Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We present an extension to the $\\mathtt{mathlib}$ library of the Lean theorem prover formalizing the foundations of computability theory. We use primitive recursive functions and partial recursive functions as the main objects of study, and we use a constructive encoding of partial functions such that they are executable when the programs in question provably halt. Main theorems include the construction of a universal partial recursive function and a proof of the undecidability of the halting problem. Type class inference provides a transparent way to supply G\\\"{o}del numberings where needed a","authors_text":"Mario Carneiro","cross_cats":["math.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2018-10-19T07:37:46Z","title":"Formalizing computability theory via partial recursive functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.08380","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:52db6dd4d31fde904cf0aa766e1fd5995aa3c3c508bdfc16108a4c4fb69bb8a8","target":"record","created_at":"2026-05-17T23:40:17Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"fee8a7ff4df6701f92e90c11478278fd1c533fb3bfd4da5c35bfa3c68218928a","cross_cats_sorted":["math.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.LO","submitted_at":"2018-10-19T07:37:46Z","title_canon_sha256":"6a85fa9dc48dbf8ee0693a6a74ca2a6b9a1a1158c80ac3458a7efc2f21349bf1"},"schema_version":"1.0","source":{"id":"1810.08380","kind":"arxiv","version":3}},"canonical_sha256":"94abeb5936400ff459be7acb04642ffd37672bce5b1c085670e67e7d79b93053","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"94abeb5936400ff459be7acb04642ffd37672bce5b1c085670e67e7d79b93053","first_computed_at":"2026-05-17T23:40:17.865614Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:40:17.865614Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7+ft5cPfr6CZHunZ2uR5fugyoWvsh9UkongCTz0g504tUhjfH25l4O6s/dKoVItWwsHfZb69LHSxEWla0EuOAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:40:17.866449Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.08380","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:52db6dd4d31fde904cf0aa766e1fd5995aa3c3c508bdfc16108a4c4fb69bb8a8","sha256:28e5742d37f33e7fa4023b5cfcc5d527a780d68411e01c043d4c1424419d903e"],"state_sha256":"094a02109d025a51d8f4f669e650a4570716bbe3257ba864c0b3f1ea857eeb27"}