{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:6TJXOE5JVHAOJ7LBXASII277KL","short_pith_number":"pith:6TJXOE5J","canonical_record":{"source":{"id":"1310.3091","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-10-11T11:48:54Z","cross_cats_sorted":[],"title_canon_sha256":"efaa9aed0947478f49f81dc75fee12a1a965b05ae014fea4d11a3fcba9889208","abstract_canon_sha256":"acbbb8ff41d5d723358043790a5f9939fb516d6dc4a53299c0970077aec4c74d"},"schema_version":"1.0"},"canonical_sha256":"f4d37713a9a9c0e4fd61b824846bff52dec49a229cf4a60485862b420bc76348","source":{"kind":"arxiv","id":"1310.3091","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.3091","created_at":"2026-05-18T00:47:21Z"},{"alias_kind":"arxiv_version","alias_value":"1310.3091v2","created_at":"2026-05-18T00:47:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.3091","created_at":"2026-05-18T00:47:21Z"},{"alias_kind":"pith_short_12","alias_value":"6TJXOE5JVHAO","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6TJXOE5JVHAOJ7LB","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6TJXOE5J","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:6TJXOE5JVHAOJ7LBXASII277KL","target":"record","payload":{"canonical_record":{"source":{"id":"1310.3091","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-10-11T11:48:54Z","cross_cats_sorted":[],"title_canon_sha256":"efaa9aed0947478f49f81dc75fee12a1a965b05ae014fea4d11a3fcba9889208","abstract_canon_sha256":"acbbb8ff41d5d723358043790a5f9939fb516d6dc4a53299c0970077aec4c74d"},"schema_version":"1.0"},"canonical_sha256":"f4d37713a9a9c0e4fd61b824846bff52dec49a229cf4a60485862b420bc76348","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:47:21.438749Z","signature_b64":"BBMRqSfcIvF19fCBwN+Me7ZxaU4UEpv9P9sq3foesVoB8Sa5/iAVphfWATzecrzhn1kICOSM6E0in8iFuXVTAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f4d37713a9a9c0e4fd61b824846bff52dec49a229cf4a60485862b420bc76348","last_reissued_at":"2026-05-18T00:47:21.438126Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:47:21.438126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.3091","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":"2026-05-18T00:47:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IdXrSjr7yiVC9u9zxaZXswe2QYKjiBNAk0zlmmM40weGUVDU1vVkZnJrLdK96BMe0luncDG5IDeat8qzJde0AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:07:38.448237Z"},"content_sha256":"e635283d14b1e72e570c63e7c6e385dac6a2c2d6b8332a747b61c164f3534766","schema_version":"1.0","event_id":"sha256:e635283d14b1e72e570c63e7c6e385dac6a2c2d6b8332a747b61c164f3534766"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:6TJXOE5JVHAOJ7LBXASII277KL","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A generalization of Levin-Schnorr's theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"Keita Yokoyama","submitted_at":"2013-10-11T11:48:54Z","abstract_excerpt":"In this paper, we will generalize the definition of partially random or complex reals, and then show the duality of random and complex, i.e., a generalized version of Levin-Schnorr's theorem. We also study randomness from the view point of arithmetic using the relativization to a complete $\\Pi^0_1$-class."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3091","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":"2026-05-18T00:47:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"do6FnFiB4YVyneN29QnGOECBtayjJUsFybY1NCwBkBQjXZ73Axm7FTsoNdDJpeT941zpMOSObCSJCoVST4SzDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:07:38.448914Z"},"content_sha256":"9c37d0b842f43d980d9069d8e6a76ae293aa3c514784f5d7c32568a8be4878f3","schema_version":"1.0","event_id":"sha256:9c37d0b842f43d980d9069d8e6a76ae293aa3c514784f5d7c32568a8be4878f3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6TJXOE5JVHAOJ7LBXASII277KL/bundle.json","state_url":"https://pith.science/pith/6TJXOE5JVHAOJ7LBXASII277KL/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6TJXOE5JVHAOJ7LBXASII277KL/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":"2026-05-26T07:07:38Z","links":{"resolver":"https://pith.science/pith/6TJXOE5JVHAOJ7LBXASII277KL","bundle":"https://pith.science/pith/6TJXOE5JVHAOJ7LBXASII277KL/bundle.json","state":"https://pith.science/pith/6TJXOE5JVHAOJ7LBXASII277KL/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6TJXOE5JVHAOJ7LBXASII277KL/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6TJXOE5JVHAOJ7LBXASII277KL","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":"acbbb8ff41d5d723358043790a5f9939fb516d6dc4a53299c0970077aec4c74d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-10-11T11:48:54Z","title_canon_sha256":"efaa9aed0947478f49f81dc75fee12a1a965b05ae014fea4d11a3fcba9889208"},"schema_version":"1.0","source":{"id":"1310.3091","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.3091","created_at":"2026-05-18T00:47:21Z"},{"alias_kind":"arxiv_version","alias_value":"1310.3091v2","created_at":"2026-05-18T00:47:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.3091","created_at":"2026-05-18T00:47:21Z"},{"alias_kind":"pith_short_12","alias_value":"6TJXOE5JVHAO","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6TJXOE5JVHAOJ7LB","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6TJXOE5J","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:9c37d0b842f43d980d9069d8e6a76ae293aa3c514784f5d7c32568a8be4878f3","target":"graph","created_at":"2026-05-18T00:47:21Z","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":"In this paper, we will generalize the definition of partially random or complex reals, and then show the duality of random and complex, i.e., a generalized version of Levin-Schnorr's theorem. We also study randomness from the view point of arithmetic using the relativization to a complete $\\Pi^0_1$-class.","authors_text":"Keita Yokoyama","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-10-11T11:48:54Z","title":"A generalization of Levin-Schnorr's theorem"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3091","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:e635283d14b1e72e570c63e7c6e385dac6a2c2d6b8332a747b61c164f3534766","target":"record","created_at":"2026-05-18T00:47:21Z","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":"acbbb8ff41d5d723358043790a5f9939fb516d6dc4a53299c0970077aec4c74d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2013-10-11T11:48:54Z","title_canon_sha256":"efaa9aed0947478f49f81dc75fee12a1a965b05ae014fea4d11a3fcba9889208"},"schema_version":"1.0","source":{"id":"1310.3091","kind":"arxiv","version":2}},"canonical_sha256":"f4d37713a9a9c0e4fd61b824846bff52dec49a229cf4a60485862b420bc76348","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f4d37713a9a9c0e4fd61b824846bff52dec49a229cf4a60485862b420bc76348","first_computed_at":"2026-05-18T00:47:21.438126Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:47:21.438126Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BBMRqSfcIvF19fCBwN+Me7ZxaU4UEpv9P9sq3foesVoB8Sa5/iAVphfWATzecrzhn1kICOSM6E0in8iFuXVTAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:47:21.438749Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.3091","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e635283d14b1e72e570c63e7c6e385dac6a2c2d6b8332a747b61c164f3534766","sha256:9c37d0b842f43d980d9069d8e6a76ae293aa3c514784f5d7c32568a8be4878f3"],"state_sha256":"05e83c4318ca982729bbfabfe2385c4bd8dadf639d31d2c2e65ce03742f54637"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4N7/BhcdMJm8SJyvoKQss/Ary6CNOPd6+R04NXWzVEkMTBNQgDlZF2qqtHVL+mrkuGGLJlngPAVhk4S8oKXhBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T07:07:38.452283Z","bundle_sha256":"655b8b7852d725d4ca99fb20cc9835e031f1e28ab7a5dfe3a200713a7b5fc117"}}