{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:63HQDIKJWKWYOZRGJTKSJLC6RC","short_pith_number":"pith:63HQDIKJ","canonical_record":{"source":{"id":"1302.7069","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-02-28T03:35:18Z","cross_cats_sorted":["cs.LG","cs.LO"],"title_canon_sha256":"cbfe8b090fd62c549469799b6bfae7521b0635acecb606266271dbd75242afa4","abstract_canon_sha256":"37aad75ecdd1bbcb03252be18f46382482a624a7713b64086fd8fffaf62c7505"},"schema_version":"1.0"},"canonical_sha256":"f6cf01a149b2ad8766264cd524ac5e889baa6949cc0f5b981ef90daadf7c98ed","source":{"kind":"arxiv","id":"1302.7069","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.7069","created_at":"2026-05-18T03:32:17Z"},{"alias_kind":"arxiv_version","alias_value":"1302.7069v1","created_at":"2026-05-18T03:32:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.7069","created_at":"2026-05-18T03:32:17Z"},{"alias_kind":"pith_short_12","alias_value":"63HQDIKJWKWY","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"63HQDIKJWKWYOZRG","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"63HQDIKJ","created_at":"2026-05-18T12:27:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:63HQDIKJWKWYOZRGJTKSJLC6RC","target":"record","payload":{"canonical_record":{"source":{"id":"1302.7069","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-02-28T03:35:18Z","cross_cats_sorted":["cs.LG","cs.LO"],"title_canon_sha256":"cbfe8b090fd62c549469799b6bfae7521b0635acecb606266271dbd75242afa4","abstract_canon_sha256":"37aad75ecdd1bbcb03252be18f46382482a624a7713b64086fd8fffaf62c7505"},"schema_version":"1.0"},"canonical_sha256":"f6cf01a149b2ad8766264cd524ac5e889baa6949cc0f5b981ef90daadf7c98ed","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:32:17.591293Z","signature_b64":"wRGvTjDNoOiLjjcWCUYQVaVrlIdMmh8QKo3fzPYGXNpsrAW2fSDRpRPmVnuAgywjPtHE+P6gqraac6vzgNb2Dw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f6cf01a149b2ad8766264cd524ac5e889baa6949cc0f5b981ef90daadf7c98ed","last_reissued_at":"2026-05-18T03:32:17.590720Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:32:17.590720Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1302.7069","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:32:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+LwRh5NmrsvWDRFyWsTYn1E8EXSdYoNijGc97mV9H3P6YZ2FEUgyZG4/Ce21FD9vMJAnNt0fXw7KEDZF1qCcAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T13:08:54.494691Z"},"content_sha256":"08a9995c9e3c410f5c998b645eed23e631c54f69a544aebd22adfce534505188","schema_version":"1.0","event_id":"sha256:08a9995c9e3c410f5c998b645eed23e631c54f69a544aebd22adfce534505188"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:63HQDIKJWKWYOZRGJTKSJLC6RC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Learning Theory in the Arithmetic Hierarchy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.LG","cs.LO"],"primary_cat":"math.LO","authors_text":"Achilles Beros","submitted_at":"2013-02-28T03:35:18Z","abstract_excerpt":"We consider the arithmetic complexity of index sets of uniformly computably enumerable families learnable under different learning criteria. We determine the exact complexity of these sets for the standard notions of finite learning, learning in the limit, behaviorally correct learning and anomalous learning in the limit. In proving the $\\Sigma_5^0$-completeness result for behaviorally correct learning we prove a result of independent interest; if a uniformly computably enumerable family is not learnable, then for any computable learner there is a $\\Delta_2^0$ enumeration witnessing failure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.7069","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:32:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4h3mGLlyvNX7a+z2Pg9PbS05M8NQa5ItPSNpbuL52cqTDuJIzHvHeVRVlVAmeFliaNFtF/8mgkxJYE9vaDrKDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T13:08:54.495044Z"},"content_sha256":"67dc2db338f5d5f2f34f930958828f6f6b9a4d7ee468721db814bc20349f2ffe","schema_version":"1.0","event_id":"sha256:67dc2db338f5d5f2f34f930958828f6f6b9a4d7ee468721db814bc20349f2ffe"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/63HQDIKJWKWYOZRGJTKSJLC6RC/bundle.json","state_url":"https://pith.science/pith/63HQDIKJWKWYOZRGJTKSJLC6RC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/63HQDIKJWKWYOZRGJTKSJLC6RC/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-22T13:08:54Z","links":{"resolver":"https://pith.science/pith/63HQDIKJWKWYOZRGJTKSJLC6RC","bundle":"https://pith.science/pith/63HQDIKJWKWYOZRGJTKSJLC6RC/bundle.json","state":"https://pith.science/pith/63HQDIKJWKWYOZRGJTKSJLC6RC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/63HQDIKJWKWYOZRGJTKSJLC6RC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:63HQDIKJWKWYOZRGJTKSJLC6RC","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":"37aad75ecdd1bbcb03252be18f46382482a624a7713b64086fd8fffaf62c7505","cross_cats_sorted":["cs.LG","cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-02-28T03:35:18Z","title_canon_sha256":"cbfe8b090fd62c549469799b6bfae7521b0635acecb606266271dbd75242afa4"},"schema_version":"1.0","source":{"id":"1302.7069","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1302.7069","created_at":"2026-05-18T03:32:17Z"},{"alias_kind":"arxiv_version","alias_value":"1302.7069v1","created_at":"2026-05-18T03:32:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1302.7069","created_at":"2026-05-18T03:32:17Z"},{"alias_kind":"pith_short_12","alias_value":"63HQDIKJWKWY","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_16","alias_value":"63HQDIKJWKWYOZRG","created_at":"2026-05-18T12:27:34Z"},{"alias_kind":"pith_short_8","alias_value":"63HQDIKJ","created_at":"2026-05-18T12:27:34Z"}],"graph_snapshots":[{"event_id":"sha256:67dc2db338f5d5f2f34f930958828f6f6b9a4d7ee468721db814bc20349f2ffe","target":"graph","created_at":"2026-05-18T03:32:17Z","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 consider the arithmetic complexity of index sets of uniformly computably enumerable families learnable under different learning criteria. We determine the exact complexity of these sets for the standard notions of finite learning, learning in the limit, behaviorally correct learning and anomalous learning in the limit. In proving the $\\Sigma_5^0$-completeness result for behaviorally correct learning we prove a result of independent interest; if a uniformly computably enumerable family is not learnable, then for any computable learner there is a $\\Delta_2^0$ enumeration witnessing failure.","authors_text":"Achilles Beros","cross_cats":["cs.LG","cs.LO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-02-28T03:35:18Z","title":"Learning Theory in the Arithmetic Hierarchy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.7069","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":"sha256:08a9995c9e3c410f5c998b645eed23e631c54f69a544aebd22adfce534505188","target":"record","created_at":"2026-05-18T03:32:17Z","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":"37aad75ecdd1bbcb03252be18f46382482a624a7713b64086fd8fffaf62c7505","cross_cats_sorted":["cs.LG","cs.LO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-02-28T03:35:18Z","title_canon_sha256":"cbfe8b090fd62c549469799b6bfae7521b0635acecb606266271dbd75242afa4"},"schema_version":"1.0","source":{"id":"1302.7069","kind":"arxiv","version":1}},"canonical_sha256":"f6cf01a149b2ad8766264cd524ac5e889baa6949cc0f5b981ef90daadf7c98ed","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f6cf01a149b2ad8766264cd524ac5e889baa6949cc0f5b981ef90daadf7c98ed","first_computed_at":"2026-05-18T03:32:17.590720Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:32:17.590720Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"wRGvTjDNoOiLjjcWCUYQVaVrlIdMmh8QKo3fzPYGXNpsrAW2fSDRpRPmVnuAgywjPtHE+P6gqraac6vzgNb2Dw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:32:17.591293Z","signed_message":"canonical_sha256_bytes"},"source_id":"1302.7069","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08a9995c9e3c410f5c998b645eed23e631c54f69a544aebd22adfce534505188","sha256:67dc2db338f5d5f2f34f930958828f6f6b9a4d7ee468721db814bc20349f2ffe"],"state_sha256":"7c075d85d4d5b5fd68928f27fe4aeee83d96436d836e6d4da27ad8b35c7a1602"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NtkCLqVzmMgle6pFcWx4HkRRMbj0RzxWE+jl+WNLqDxJCHHqdRdbl79znQOmgVFETsbuCoe6sW01IS2tiOmsBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T13:08:54.496993Z","bundle_sha256":"73b6a0097f0bbd9b9937100095c99bda9d2590dc762afb0b6036007c44252ed9"}}