{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:XJG2M2D2GXWANJ2NOCZ2TWX6XS","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":"4892283a0a7e106d5faa00a053b5617c2e41fb16063ffbcf77dba0278949b972","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-19T05:47:42Z","title_canon_sha256":"2f49bf6848fa337314eac5e81a70ce1efb843daa5e5d535ac94551aeb6b8e7e3"},"schema_version":"1.0","source":{"id":"1207.4556","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1207.4556","created_at":"2026-05-18T03:35:38Z"},{"alias_kind":"arxiv_version","alias_value":"1207.4556v2","created_at":"2026-05-18T03:35:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1207.4556","created_at":"2026-05-18T03:35:38Z"},{"alias_kind":"pith_short_12","alias_value":"XJG2M2D2GXWA","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"XJG2M2D2GXWANJ2N","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"XJG2M2D2","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:70d8853405117637d2ade64e5eadacda63a367ec1b6e1e3b12386d3664dd87ab","target":"graph","created_at":"2026-05-18T03:35:38Z","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 complexity of the Quicksort algorithm is usually measured by the number of key comparisons used during its execution. When operating on a list of $n$ data, permuted uniformly at random, the appropriately normalized complexity $Y_n$ is known to converge almost surely to a non-degenerate random limit $Y$. This assumes a natural embedding of all $Y_n$ on one probability space, e.g., via random binary search trees. In this note a central limit theorem for the error term in the latter almost sure convergence is shown: $$\\sqrt{\\frac{n}{2\\log n}}(Y_n-Y) \\stackrel{d}{\\longrightarrow} {\\cal N} \\qqu","authors_text":"Ralph Neininger","cross_cats":["cs.DS"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-19T05:47:42Z","title":"Refined Quicksort asymptotics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.4556","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:afe1a641cb5b2bce9465c0a2b0a47bb32bf88aad0636568100f2a08d3252a0b6","target":"record","created_at":"2026-05-18T03:35:38Z","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":"4892283a0a7e106d5faa00a053b5617c2e41fb16063ffbcf77dba0278949b972","cross_cats_sorted":["cs.DS"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-07-19T05:47:42Z","title_canon_sha256":"2f49bf6848fa337314eac5e81a70ce1efb843daa5e5d535ac94551aeb6b8e7e3"},"schema_version":"1.0","source":{"id":"1207.4556","kind":"arxiv","version":2}},"canonical_sha256":"ba4da6687a35ec06a74d70b3a9dafebcbc53a898e5cbfdaa05558d8fbf5355de","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ba4da6687a35ec06a74d70b3a9dafebcbc53a898e5cbfdaa05558d8fbf5355de","first_computed_at":"2026-05-18T03:35:38.405167Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:35:38.405167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OThTDyxFogLcKSNJRIIxtQyt5Jg3AjDUEGVTU3DdRVmjfc7/MC7rVx5zugYUNRpSGuuV62YRFv5cy67Q+Ek/AA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:35:38.405880Z","signed_message":"canonical_sha256_bytes"},"source_id":"1207.4556","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:afe1a641cb5b2bce9465c0a2b0a47bb32bf88aad0636568100f2a08d3252a0b6","sha256:70d8853405117637d2ade64e5eadacda63a367ec1b6e1e3b12386d3664dd87ab"],"state_sha256":"ca92ea5b8152f6ab880d65fe0171ba78c9a2a89c3ddd5b95bd8da24b2e32ed1d"}