{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:4H3MUTQPYIZA2CZ4W7IL2S2YWS","short_pith_number":"pith:4H3MUTQP","canonical_record":{"source":{"id":"1008.4825","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2010-08-28T01:17:15Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"e0b8bb7c6d4902601827df88176d8a0ff7cf96682797bbf0fb0fe2d17440f2ad","abstract_canon_sha256":"aee9568663360d204cd3f2b9130fadfd7cc041ef9c9f1e968bb8e9739776834c"},"schema_version":"1.0"},"canonical_sha256":"e1f6ca4e0fc2320d0b3cb7d0bd4b58b49b582b6ec25f361f806a83ebc0fa603e","source":{"kind":"arxiv","id":"1008.4825","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.4825","created_at":"2026-05-18T02:45:21Z"},{"alias_kind":"arxiv_version","alias_value":"1008.4825v2","created_at":"2026-05-18T02:45:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.4825","created_at":"2026-05-18T02:45:21Z"},{"alias_kind":"pith_short_12","alias_value":"4H3MUTQPYIZA","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"4H3MUTQPYIZA2CZ4","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"4H3MUTQP","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:4H3MUTQPYIZA2CZ4W7IL2S2YWS","target":"record","payload":{"canonical_record":{"source":{"id":"1008.4825","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2010-08-28T01:17:15Z","cross_cats_sorted":["cs.CC"],"title_canon_sha256":"e0b8bb7c6d4902601827df88176d8a0ff7cf96682797bbf0fb0fe2d17440f2ad","abstract_canon_sha256":"aee9568663360d204cd3f2b9130fadfd7cc041ef9c9f1e968bb8e9739776834c"},"schema_version":"1.0"},"canonical_sha256":"e1f6ca4e0fc2320d0b3cb7d0bd4b58b49b582b6ec25f361f806a83ebc0fa603e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:21.779901Z","signature_b64":"ZWRiA2wquHALlwtWSkJCUZi+Ecowol58R9Geb4DJtuq5My6i52QVofiqKy4Zs9Yy7btjiQEH43PdhvZqxQdbDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e1f6ca4e0fc2320d0b3cb7d0bd4b58b49b582b6ec25f361f806a83ebc0fa603e","last_reissued_at":"2026-05-18T02:45:21.779348Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:21.779348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1008.4825","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:45:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4P6MWRZc3jkj5DBr6LEAzflyfDVU+2w0PX8RDSSr/Botf/68bphn7aVsWOrdZoCXamkaZjjiVE5Y0344+kyCCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:46:03.600663Z"},"content_sha256":"f199cc22d762803015eb78825cf3e44fdb6fab72446ebc854983c4a7574119cd","schema_version":"1.0","event_id":"sha256:f199cc22d762803015eb78825cf3e44fdb6fab72446ebc854983c4a7574119cd"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:4H3MUTQPYIZA2CZ4W7IL2S2YWS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Arithmetic complexity via effective names for random sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CC"],"primary_cat":"math.LO","authors_text":"Bj{\\o}rn Kjos-Hanssen, Frank Stephan, Jason R. Teutsch","submitted_at":"2010-08-28T01:17:15Z","abstract_excerpt":"We investigate enumerability properties for classes of sets which permit recursive, lexicographically increasing approximations, or left-r.e. sets. In addition to pinpointing the complexity of left-r.e. Martin-L\\\"{o}f, computably, Schnorr, and Kurtz random sets, weakly 1-generics and their complementary classes, we find that there exist characterizations of the third and fourth levels of the arithmetic hierarchy purely in terms of these notions.\n  More generally, there exists an equivalence between arithmetic complexity and existence of numberings for classes of left-r.e. sets with shift-persi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4825","kind":"arxiv","version":2},"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":"2026-05-18T02:45:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"73ASzvoUWhBZHO6poFQaQ2m2nCItSaPxOZVApECny2AgqunAkp6LxOD4/n240C8MyZl4EceKEcpMYxGXW/8XCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T13:46:03.601019Z"},"content_sha256":"4ea2b96655322aacec1603a4b7f4c97cfe18738c4877943dc9296afaa44b3f84","schema_version":"1.0","event_id":"sha256:4ea2b96655322aacec1603a4b7f4c97cfe18738c4877943dc9296afaa44b3f84"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/4H3MUTQPYIZA2CZ4W7IL2S2YWS/bundle.json","state_url":"https://pith.science/pith/4H3MUTQPYIZA2CZ4W7IL2S2YWS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/4H3MUTQPYIZA2CZ4W7IL2S2YWS/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":"2026-05-27T13:46:03Z","links":{"resolver":"https://pith.science/pith/4H3MUTQPYIZA2CZ4W7IL2S2YWS","bundle":"https://pith.science/pith/4H3MUTQPYIZA2CZ4W7IL2S2YWS/bundle.json","state":"https://pith.science/pith/4H3MUTQPYIZA2CZ4W7IL2S2YWS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/4H3MUTQPYIZA2CZ4W7IL2S2YWS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:4H3MUTQPYIZA2CZ4W7IL2S2YWS","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":"aee9568663360d204cd3f2b9130fadfd7cc041ef9c9f1e968bb8e9739776834c","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2010-08-28T01:17:15Z","title_canon_sha256":"e0b8bb7c6d4902601827df88176d8a0ff7cf96682797bbf0fb0fe2d17440f2ad"},"schema_version":"1.0","source":{"id":"1008.4825","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1008.4825","created_at":"2026-05-18T02:45:21Z"},{"alias_kind":"arxiv_version","alias_value":"1008.4825v2","created_at":"2026-05-18T02:45:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1008.4825","created_at":"2026-05-18T02:45:21Z"},{"alias_kind":"pith_short_12","alias_value":"4H3MUTQPYIZA","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"4H3MUTQPYIZA2CZ4","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"4H3MUTQP","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:4ea2b96655322aacec1603a4b7f4c97cfe18738c4877943dc9296afaa44b3f84","target":"graph","created_at":"2026-05-18T02:45:21Z","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 investigate enumerability properties for classes of sets which permit recursive, lexicographically increasing approximations, or left-r.e. sets. In addition to pinpointing the complexity of left-r.e. Martin-L\\\"{o}f, computably, Schnorr, and Kurtz random sets, weakly 1-generics and their complementary classes, we find that there exist characterizations of the third and fourth levels of the arithmetic hierarchy purely in terms of these notions.\n  More generally, there exists an equivalence between arithmetic complexity and existence of numberings for classes of left-r.e. sets with shift-persi","authors_text":"Bj{\\o}rn Kjos-Hanssen, Frank Stephan, Jason R. Teutsch","cross_cats":["cs.CC"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2010-08-28T01:17:15Z","title":"Arithmetic complexity via effective names for random sequences"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.4825","kind":"arxiv","version":2},"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:f199cc22d762803015eb78825cf3e44fdb6fab72446ebc854983c4a7574119cd","target":"record","created_at":"2026-05-18T02:45:21Z","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":"aee9568663360d204cd3f2b9130fadfd7cc041ef9c9f1e968bb8e9739776834c","cross_cats_sorted":["cs.CC"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2010-08-28T01:17:15Z","title_canon_sha256":"e0b8bb7c6d4902601827df88176d8a0ff7cf96682797bbf0fb0fe2d17440f2ad"},"schema_version":"1.0","source":{"id":"1008.4825","kind":"arxiv","version":2}},"canonical_sha256":"e1f6ca4e0fc2320d0b3cb7d0bd4b58b49b582b6ec25f361f806a83ebc0fa603e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e1f6ca4e0fc2320d0b3cb7d0bd4b58b49b582b6ec25f361f806a83ebc0fa603e","first_computed_at":"2026-05-18T02:45:21.779348Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:45:21.779348Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZWRiA2wquHALlwtWSkJCUZi+Ecowol58R9Geb4DJtuq5My6i52QVofiqKy4Zs9Yy7btjiQEH43PdhvZqxQdbDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:45:21.779901Z","signed_message":"canonical_sha256_bytes"},"source_id":"1008.4825","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f199cc22d762803015eb78825cf3e44fdb6fab72446ebc854983c4a7574119cd","sha256:4ea2b96655322aacec1603a4b7f4c97cfe18738c4877943dc9296afaa44b3f84"],"state_sha256":"54172ac67b63105e4225fc53a9159ed7567df4420805581c2c223f2f97baea95"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fyPVvb92eRkG22pnVTzzVDkeLGQxFvUX1MMhZDLSyfiMfAhFjvqHdKOyCMTX+hVA10nEx1RtEMaUKtsmwO+CAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T13:46:03.603461Z","bundle_sha256":"f6cfba5f07c4cf23a6060b2784cdb23d0d57d2014771ff1325a14d6e6e730f57"}}