{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:6C6LFGDOW4SLHPXWHJROYOINLX","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":"cc7b59e017a703ad958e7d3010a986c289af6f86061e69f01fb19e884a0f8cc3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.CC","submitted_at":"2012-02-29T20:09:17Z","title_canon_sha256":"bf08417e3e6cd30de144b0064ae5a83261c440cf2dd4bcb2f9051bcec8552999"},"schema_version":"1.0","source":{"id":"1202.6668","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1202.6668","created_at":"2026-05-18T03:26:39Z"},{"alias_kind":"arxiv_version","alias_value":"1202.6668v2","created_at":"2026-05-18T03:26:39Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1202.6668","created_at":"2026-05-18T03:26:39Z"},{"alias_kind":"pith_short_12","alias_value":"6C6LFGDOW4SL","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_16","alias_value":"6C6LFGDOW4SLHPXW","created_at":"2026-05-18T12:26:56Z"},{"alias_kind":"pith_short_8","alias_value":"6C6LFGDO","created_at":"2026-05-18T12:26:56Z"}],"graph_snapshots":[{"event_id":"sha256:fcdaee5f61912e7bbf98975f936b43e326d4a128a5a6e900a15a17015b21c8fd","target":"graph","created_at":"2026-05-18T03:26:39Z","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":"Peter Gacs showed (Gacs 1974) that for every n there exists a bit string x of length n whose plain complexity C(x) has almost maximal conditional complexity relative to x, i.e., C(C(x)|x) > log n - log^(2) n - O(1). (Here log^(2) i = log log i.) Following Elena Kalinina (Kalinina 2011), we provide a simple game-based proof of this result; modifying her argument, we get a better (and tight) bound log n - O(1). We also show the same bound for prefix-free complexity.\n  Robert Solovay showed (Solovay 1975) that infinitely many strings x have maximal plain complexity but not maximal prefix complexi","authors_text":"Alexander Shen, Bruno Bauwens","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.CC","submitted_at":"2012-02-29T20:09:17Z","title":"Complexity of complexity and strings with maximal plain and prefix Kolmogorov complexity"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1202.6668","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":"sha256:9bcc5cdbc4b4b69ee4ea74551e047cc06275562d8c8f4ed86d7ca67617b1da03","target":"record","created_at":"2026-05-18T03:26:39Z","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":"cc7b59e017a703ad958e7d3010a986c289af6f86061e69f01fb19e884a0f8cc3","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/3.0/","primary_cat":"cs.CC","submitted_at":"2012-02-29T20:09:17Z","title_canon_sha256":"bf08417e3e6cd30de144b0064ae5a83261c440cf2dd4bcb2f9051bcec8552999"},"schema_version":"1.0","source":{"id":"1202.6668","kind":"arxiv","version":2}},"canonical_sha256":"f0bcb2986eb724b3bef63a62ec390d5de89670189cae41d98b2655c871a5bc06","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f0bcb2986eb724b3bef63a62ec390d5de89670189cae41d98b2655c871a5bc06","first_computed_at":"2026-05-18T03:26:39.594199Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:26:39.594199Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"BNQesm2ItSlONHA6e0qimk+tlLWPVzcG11XKGNadUVcq7iYaSTwJWw9J2Kyam48hVjbjIoe/kqBUMMayFJ1BDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:26:39.594653Z","signed_message":"canonical_sha256_bytes"},"source_id":"1202.6668","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9bcc5cdbc4b4b69ee4ea74551e047cc06275562d8c8f4ed86d7ca67617b1da03","sha256:fcdaee5f61912e7bbf98975f936b43e326d4a128a5a6e900a15a17015b21c8fd"],"state_sha256":"eeb96713ce24bc2623afc18510c721718ab29f77ff5a1747acd5075c849d838a"}