{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:MUVLIBT7M5DT7J5RNJP2BY4DF2","short_pith_number":"pith:MUVLIBT7","schema_version":"1.0","canonical_sha256":"652ab4067f67473fa7b16a5fa0e3832e926e0dee38957357a504084a7d343709","source":{"kind":"arxiv","id":"1310.5230","version":1},"attestation_state":"computed","paper":{"title":"Prefix and plain Kolmogorov complexity characterizations of 2-randomness: simple proofs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Bruno Bauwens","submitted_at":"2013-10-19T13:42:18Z","abstract_excerpt":"Joseph Miller [16] and independently Andre Nies, Frank Stephan and Sebastiaan Terwijn [18] gave a complexity characterization of 2-random sequences in terms of plain Kolmogorov complexity C: they are sequences that have infinitely many initial segments with O(1)-maximal plain complexity (among the strings of the same length). Later Miller [17] showed that prefix complexity K can also be used in a similar way: a sequence is 2-random if and only if it has infinitely many initial segments with O(1)-maximal prefix complexity (which is n + K (n) for strings of length n). The known proofs of these r"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1310.5230","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.IT","submitted_at":"2013-10-19T13:42:18Z","cross_cats_sorted":["math.IT"],"title_canon_sha256":"6adfaf70d377e58c4944e785300addfff8f7014d1c601782608fa0e67f81bb2f","abstract_canon_sha256":"ffb16ac944d315bfbb23f22bdc5112098e2aa403bd586f019dc448325299a1e0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:46.570830Z","signature_b64":"hkrknAibI4m3JDvIkt6ZT03RWF7W0CHViymQCot6GWtJZ2B0PabxUFjoYnh5bGWp0gTOquTDRjvw+ZsiuaBRAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"652ab4067f67473fa7b16a5fa0e3832e926e0dee38957357a504084a7d343709","last_reissued_at":"2026-05-18T03:09:46.569987Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:46.569987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Prefix and plain Kolmogorov complexity characterizations of 2-randomness: simple proofs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Bruno Bauwens","submitted_at":"2013-10-19T13:42:18Z","abstract_excerpt":"Joseph Miller [16] and independently Andre Nies, Frank Stephan and Sebastiaan Terwijn [18] gave a complexity characterization of 2-random sequences in terms of plain Kolmogorov complexity C: they are sequences that have infinitely many initial segments with O(1)-maximal plain complexity (among the strings of the same length). Later Miller [17] showed that prefix complexity K can also be used in a similar way: a sequence is 2-random if and only if it has infinitely many initial segments with O(1)-maximal prefix complexity (which is n + K (n) for strings of length n). The known proofs of these r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5230","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1310.5230","created_at":"2026-05-18T03:09:46.570118+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.5230v1","created_at":"2026-05-18T03:09:46.570118+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.5230","created_at":"2026-05-18T03:09:46.570118+00:00"},{"alias_kind":"pith_short_12","alias_value":"MUVLIBT7M5DT","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_16","alias_value":"MUVLIBT7M5DT7J5R","created_at":"2026-05-18T12:27:52.871228+00:00"},{"alias_kind":"pith_short_8","alias_value":"MUVLIBT7","created_at":"2026-05-18T12:27:52.871228+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MUVLIBT7M5DT7J5RNJP2BY4DF2","json":"https://pith.science/pith/MUVLIBT7M5DT7J5RNJP2BY4DF2.json","graph_json":"https://pith.science/api/pith-number/MUVLIBT7M5DT7J5RNJP2BY4DF2/graph.json","events_json":"https://pith.science/api/pith-number/MUVLIBT7M5DT7J5RNJP2BY4DF2/events.json","paper":"https://pith.science/paper/MUVLIBT7"},"agent_actions":{"view_html":"https://pith.science/pith/MUVLIBT7M5DT7J5RNJP2BY4DF2","download_json":"https://pith.science/pith/MUVLIBT7M5DT7J5RNJP2BY4DF2.json","view_paper":"https://pith.science/paper/MUVLIBT7","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.5230&json=true","fetch_graph":"https://pith.science/api/pith-number/MUVLIBT7M5DT7J5RNJP2BY4DF2/graph.json","fetch_events":"https://pith.science/api/pith-number/MUVLIBT7M5DT7J5RNJP2BY4DF2/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MUVLIBT7M5DT7J5RNJP2BY4DF2/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MUVLIBT7M5DT7J5RNJP2BY4DF2/action/storage_attestation","attest_author":"https://pith.science/pith/MUVLIBT7M5DT7J5RNJP2BY4DF2/action/author_attestation","sign_citation":"https://pith.science/pith/MUVLIBT7M5DT7J5RNJP2BY4DF2/action/citation_signature","submit_replication":"https://pith.science/pith/MUVLIBT7M5DT7J5RNJP2BY4DF2/action/replication_record"}},"created_at":"2026-05-18T03:09:46.570118+00:00","updated_at":"2026-05-18T03:09:46.570118+00:00"}