{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:GGWBTUQ5DYH3EWT4ZNC3PZCTG4","short_pith_number":"pith:GGWBTUQ5","schema_version":"1.0","canonical_sha256":"31ac19d21d1e0fb25a7ccb45b7e4533705de21e96d5692324e54930824670f07","source":{"kind":"arxiv","id":"1307.5521","version":1},"attestation_state":"computed","paper":{"title":"Realizability Interpretation of PA by Iterated Limiting PCA","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Yohji Akama","submitted_at":"2013-07-21T11:45:30Z","abstract_excerpt":"For any partial combinatory algebra (PCA for short) A, the class of A-representable partial functions from N to A quotiented by the filter of cofinite sets of N, is a PCA such that the representable partial functions are exactly the limiting partial functions of A-representable partial functions(Akama, \"Limiting partial combinatory algebras\" Theoret. Comput. Sci. Vol.311 2004). The n-times iteration of this construction results in a PCA that represents any n-iterated limiting partial recursive functions, and the inductive limit of the PCAs over all n is a PCA that represents any arithmetical, "},"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":"1307.5521","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-07-21T11:45:30Z","cross_cats_sorted":[],"title_canon_sha256":"d96c0ed50b5d9ead51095ef8fe88d2b313ed055b8228be8510df4dc534a3a8d2","abstract_canon_sha256":"850c0b9e4e4d9fb471b7e3b9a6e69032cd7bd45fd47413b544a8d0a18334c0ae"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:53:15.232334Z","signature_b64":"Zk20AfK18qDa7hQLskadYfq2e1FdIfzfDZwwI81X80TiC0Hwt3bVsDDH0utvqIvKM/yv6yHqxc4Odk1bub0WBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"31ac19d21d1e0fb25a7ccb45b7e4533705de21e96d5692324e54930824670f07","last_reissued_at":"2026-05-17T23:53:15.231820Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:53:15.231820Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Realizability Interpretation of PA by Iterated Limiting PCA","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Yohji Akama","submitted_at":"2013-07-21T11:45:30Z","abstract_excerpt":"For any partial combinatory algebra (PCA for short) A, the class of A-representable partial functions from N to A quotiented by the filter of cofinite sets of N, is a PCA such that the representable partial functions are exactly the limiting partial functions of A-representable partial functions(Akama, \"Limiting partial combinatory algebras\" Theoret. Comput. Sci. Vol.311 2004). The n-times iteration of this construction results in a PCA that represents any n-iterated limiting partial recursive functions, and the inductive limit of the PCAs over all n is a PCA that represents any arithmetical, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.5521","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":""},"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":"1307.5521","created_at":"2026-05-17T23:53:15.231902+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.5521v1","created_at":"2026-05-17T23:53:15.231902+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.5521","created_at":"2026-05-17T23:53:15.231902+00:00"},{"alias_kind":"pith_short_12","alias_value":"GGWBTUQ5DYH3","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_16","alias_value":"GGWBTUQ5DYH3EWT4","created_at":"2026-05-18T12:27:45.050594+00:00"},{"alias_kind":"pith_short_8","alias_value":"GGWBTUQ5","created_at":"2026-05-18T12:27:45.050594+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/GGWBTUQ5DYH3EWT4ZNC3PZCTG4","json":"https://pith.science/pith/GGWBTUQ5DYH3EWT4ZNC3PZCTG4.json","graph_json":"https://pith.science/api/pith-number/GGWBTUQ5DYH3EWT4ZNC3PZCTG4/graph.json","events_json":"https://pith.science/api/pith-number/GGWBTUQ5DYH3EWT4ZNC3PZCTG4/events.json","paper":"https://pith.science/paper/GGWBTUQ5"},"agent_actions":{"view_html":"https://pith.science/pith/GGWBTUQ5DYH3EWT4ZNC3PZCTG4","download_json":"https://pith.science/pith/GGWBTUQ5DYH3EWT4ZNC3PZCTG4.json","view_paper":"https://pith.science/paper/GGWBTUQ5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.5521&json=true","fetch_graph":"https://pith.science/api/pith-number/GGWBTUQ5DYH3EWT4ZNC3PZCTG4/graph.json","fetch_events":"https://pith.science/api/pith-number/GGWBTUQ5DYH3EWT4ZNC3PZCTG4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GGWBTUQ5DYH3EWT4ZNC3PZCTG4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GGWBTUQ5DYH3EWT4ZNC3PZCTG4/action/storage_attestation","attest_author":"https://pith.science/pith/GGWBTUQ5DYH3EWT4ZNC3PZCTG4/action/author_attestation","sign_citation":"https://pith.science/pith/GGWBTUQ5DYH3EWT4ZNC3PZCTG4/action/citation_signature","submit_replication":"https://pith.science/pith/GGWBTUQ5DYH3EWT4ZNC3PZCTG4/action/replication_record"}},"created_at":"2026-05-17T23:53:15.231902+00:00","updated_at":"2026-05-17T23:53:15.231902+00:00"}