{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NMAFNNFKDDPVWAD2RQC7G2AS6L","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":"d9d70c4b8e9699634cc9b92cfae4b6a47b870c33655b50c9d9e8546ef3c010dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-05-13T16:17:03Z","title_canon_sha256":"9b8a9715b1ca17f9e1d1ed8ab697033a40e7ee4f45274238571f890149ad0e99"},"schema_version":"1.0","source":{"id":"1205.2879","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1205.2879","created_at":"2026-05-18T03:55:45Z"},{"alias_kind":"arxiv_version","alias_value":"1205.2879v1","created_at":"2026-05-18T03:55:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1205.2879","created_at":"2026-05-18T03:55:45Z"},{"alias_kind":"pith_short_12","alias_value":"NMAFNNFKDDPV","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NMAFNNFKDDPVWAD2","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NMAFNNFK","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:e1e0951436b9bd6098794ed23349f04a07ba30ab1365e8234abd1094f8653be9","target":"graph","created_at":"2026-05-18T03:55:45Z","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 a simplified and streamlined characterisation of provably total computable functions of the theory ID_1 of non-iterated inductive definitions. The idea of the simplification is to employ the method of operator-controlled derivations that was originally introduced by Wilfried Buchholz and afterwards applied by the second author to a characterisation of provably total computable functions of Peano arithmetic PA.","authors_text":"Andreas Weiermann, Naohi Eguchi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-05-13T16:17:03Z","title":"A Simplified Characterisation of Provably Computable Functions of the System ID_1 of Inductive Definitions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.2879","kind":"arxiv","version":1},"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":"sha256:90d5f9eb58d70db2e696f87c39d9a142a05f872be970ab801304f28c4bf77d81","target":"record","created_at":"2026-05-18T03:55:45Z","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":"d9d70c4b8e9699634cc9b92cfae4b6a47b870c33655b50c9d9e8546ef3c010dc","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-05-13T16:17:03Z","title_canon_sha256":"9b8a9715b1ca17f9e1d1ed8ab697033a40e7ee4f45274238571f890149ad0e99"},"schema_version":"1.0","source":{"id":"1205.2879","kind":"arxiv","version":1}},"canonical_sha256":"6b0056b4aa18df5b007a8c05f36812f2e1f4b2896d66b400a690061c745f0843","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6b0056b4aa18df5b007a8c05f36812f2e1f4b2896d66b400a690061c745f0843","first_computed_at":"2026-05-18T03:55:45.766213Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:55:45.766213Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"gvQ9Rz8dka0yus67Q50DQldZL7fBQsye5zFtvLoacKc07p0XyFOLyd7z3LvU31K476vtJ8Fli3fHb8BZcMAqDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:55:45.766825Z","signed_message":"canonical_sha256_bytes"},"source_id":"1205.2879","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:90d5f9eb58d70db2e696f87c39d9a142a05f872be970ab801304f28c4bf77d81","sha256:e1e0951436b9bd6098794ed23349f04a07ba30ab1365e8234abd1094f8653be9"],"state_sha256":"84c5f5d00b1b8e97e547066da2df0e1d7fc9a76ccaa97df9efd3d0545a228f39"}