{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:RWLWIMM7RWHNGPK5QMHA5DGOPS","short_pith_number":"pith:RWLWIMM7","canonical_record":{"source":{"id":"1204.0201","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-04-01T11:59:02Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"48338a830348c447ad55724dc6e3e01c6aff8012921a85676c8b8d6919b44aa1","abstract_canon_sha256":"3b30c61d65f3eaf9a1d830ebe5e421c61ffdcda80ea49bc5e5517e3f34f3c274"},"schema_version":"1.0"},"canonical_sha256":"8d9764319f8d8ed33d5d830e0e8cce7cb2696cfe51f223570af0080f2fe653ee","source":{"kind":"arxiv","id":"1204.0201","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.0201","created_at":"2026-05-18T03:58:50Z"},{"alias_kind":"arxiv_version","alias_value":"1204.0201v1","created_at":"2026-05-18T03:58:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.0201","created_at":"2026-05-18T03:58:50Z"},{"alias_kind":"pith_short_12","alias_value":"RWLWIMM7RWHN","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RWLWIMM7RWHNGPK5","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RWLWIMM7","created_at":"2026-05-18T12:27:20Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:RWLWIMM7RWHNGPK5QMHA5DGOPS","target":"record","payload":{"canonical_record":{"source":{"id":"1204.0201","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-04-01T11:59:02Z","cross_cats_sorted":["cs.IT","math.IT"],"title_canon_sha256":"48338a830348c447ad55724dc6e3e01c6aff8012921a85676c8b8d6919b44aa1","abstract_canon_sha256":"3b30c61d65f3eaf9a1d830ebe5e421c61ffdcda80ea49bc5e5517e3f34f3c274"},"schema_version":"1.0"},"canonical_sha256":"8d9764319f8d8ed33d5d830e0e8cce7cb2696cfe51f223570af0080f2fe653ee","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:58:50.008842Z","signature_b64":"aTGWt6mt0T724KmHxRUf2dy3+8SoPezmI2slVH9cSluMFY3wu+TVUYX7VIQSrQsqgaKVPT3m5dyAhNTrur8ECQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8d9764319f8d8ed33d5d830e0e8cce7cb2696cfe51f223570af0080f2fe653ee","last_reissued_at":"2026-05-18T03:58:50.008015Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:58:50.008015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1204.0201","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":"2026-05-18T03:58:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"gJjzRd+fkmCY/1XoXGbrEV5JJgHEar4uXDVAekExWB7Np6WVicYMdpy7j7CXn7k1MMvlfKYQhYmEkfIdjjDcCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:05:22.333504Z"},"content_sha256":"ca8225274e68904a08a5d6653b269e44f8cb29c2cc3ccde02754d4a18e133f4c","schema_version":"1.0","event_id":"sha256:ca8225274e68904a08a5d6653b269e44f8cb29c2cc3ccde02754d4a18e133f4c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:RWLWIMM7RWHNGPK5QMHA5DGOPS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Limit complexities revisited [once more]","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.IT","math.IT"],"primary_cat":"math.LO","authors_text":"Alexander Shen, Andrej Muchnik, Laurent Bienvenu, Nikolai Vereshchagin","submitted_at":"2012-04-01T11:59:02Z","abstract_excerpt":"The main goal of this article is to put some known results in a common perspective and to simplify their proofs.\n  We start with a simple proof of a result of Vereshchagin saying that $\\limsup_n C(x|n)$ equals $C^{0'}(x)$. Then we use the same argument to prove similar results for prefix complexity, a priori probability on binary tree, to prove Conidis' theorem about limits of effectively open sets, and also to improve the results of Muchnik about limit frequencies. As a by-product, we get a criterion of 2-randomness proved by Miller: a sequence $X$ is 2-random if and only if there exists $c$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0201","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":"2026-05-18T03:58:50Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2IdJiL7jMOGHbWh35GOSv9+lQ71CGzPSRRGfyi+Aqq7az6jkhrgFq9caqeQMncGbPLJumQj1PzZNz+KHCW7FDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T07:05:22.334126Z"},"content_sha256":"2ee5322d963e9bdbd32ff0f884444cb25ec140db7979d9fbbf3816ceedcd7b75","schema_version":"1.0","event_id":"sha256:2ee5322d963e9bdbd32ff0f884444cb25ec140db7979d9fbbf3816ceedcd7b75"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RWLWIMM7RWHNGPK5QMHA5DGOPS/bundle.json","state_url":"https://pith.science/pith/RWLWIMM7RWHNGPK5QMHA5DGOPS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RWLWIMM7RWHNGPK5QMHA5DGOPS/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":"2026-05-26T07:05:22Z","links":{"resolver":"https://pith.science/pith/RWLWIMM7RWHNGPK5QMHA5DGOPS","bundle":"https://pith.science/pith/RWLWIMM7RWHNGPK5QMHA5DGOPS/bundle.json","state":"https://pith.science/pith/RWLWIMM7RWHNGPK5QMHA5DGOPS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RWLWIMM7RWHNGPK5QMHA5DGOPS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:RWLWIMM7RWHNGPK5QMHA5DGOPS","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":"3b30c61d65f3eaf9a1d830ebe5e421c61ffdcda80ea49bc5e5517e3f34f3c274","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-04-01T11:59:02Z","title_canon_sha256":"48338a830348c447ad55724dc6e3e01c6aff8012921a85676c8b8d6919b44aa1"},"schema_version":"1.0","source":{"id":"1204.0201","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1204.0201","created_at":"2026-05-18T03:58:50Z"},{"alias_kind":"arxiv_version","alias_value":"1204.0201v1","created_at":"2026-05-18T03:58:50Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1204.0201","created_at":"2026-05-18T03:58:50Z"},{"alias_kind":"pith_short_12","alias_value":"RWLWIMM7RWHN","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_16","alias_value":"RWLWIMM7RWHNGPK5","created_at":"2026-05-18T12:27:20Z"},{"alias_kind":"pith_short_8","alias_value":"RWLWIMM7","created_at":"2026-05-18T12:27:20Z"}],"graph_snapshots":[{"event_id":"sha256:2ee5322d963e9bdbd32ff0f884444cb25ec140db7979d9fbbf3816ceedcd7b75","target":"graph","created_at":"2026-05-18T03:58:50Z","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":"The main goal of this article is to put some known results in a common perspective and to simplify their proofs.\n  We start with a simple proof of a result of Vereshchagin saying that $\\limsup_n C(x|n)$ equals $C^{0'}(x)$. Then we use the same argument to prove similar results for prefix complexity, a priori probability on binary tree, to prove Conidis' theorem about limits of effectively open sets, and also to improve the results of Muchnik about limit frequencies. As a by-product, we get a criterion of 2-randomness proved by Miller: a sequence $X$ is 2-random if and only if there exists $c$ ","authors_text":"Alexander Shen, Andrej Muchnik, Laurent Bienvenu, Nikolai Vereshchagin","cross_cats":["cs.IT","math.IT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-04-01T11:59:02Z","title":"Limit complexities revisited [once more]"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.0201","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:ca8225274e68904a08a5d6653b269e44f8cb29c2cc3ccde02754d4a18e133f4c","target":"record","created_at":"2026-05-18T03:58:50Z","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":"3b30c61d65f3eaf9a1d830ebe5e421c61ffdcda80ea49bc5e5517e3f34f3c274","cross_cats_sorted":["cs.IT","math.IT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.LO","submitted_at":"2012-04-01T11:59:02Z","title_canon_sha256":"48338a830348c447ad55724dc6e3e01c6aff8012921a85676c8b8d6919b44aa1"},"schema_version":"1.0","source":{"id":"1204.0201","kind":"arxiv","version":1}},"canonical_sha256":"8d9764319f8d8ed33d5d830e0e8cce7cb2696cfe51f223570af0080f2fe653ee","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8d9764319f8d8ed33d5d830e0e8cce7cb2696cfe51f223570af0080f2fe653ee","first_computed_at":"2026-05-18T03:58:50.008015Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:58:50.008015Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"aTGWt6mt0T724KmHxRUf2dy3+8SoPezmI2slVH9cSluMFY3wu+TVUYX7VIQSrQsqgaKVPT3m5dyAhNTrur8ECQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:58:50.008842Z","signed_message":"canonical_sha256_bytes"},"source_id":"1204.0201","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ca8225274e68904a08a5d6653b269e44f8cb29c2cc3ccde02754d4a18e133f4c","sha256:2ee5322d963e9bdbd32ff0f884444cb25ec140db7979d9fbbf3816ceedcd7b75"],"state_sha256":"88ba26a0cd253fc1bcd096cd840f67266e00c10da7dc156633739cab66c92ea9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W+qlmGd0VAnkJOwbZDF1pkS2n5/MF8bvbrf+Whz/9oS/pPkGyjsf9eQcNd+QHpjlVPsiWm2StDbGkBzx4/M2Cg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T07:05:22.337502Z","bundle_sha256":"e9ecef3cacb2a8c5e452d3efd151621ab2c85b1e17a9ea056102c083481c9a06"}}