{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:VWZ67DIU5WQ4O7S42ZN3GEAWN5","short_pith_number":"pith:VWZ67DIU","canonical_record":{"source":{"id":"1403.6602","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-03-26T09:37:30Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"5cc89a8607ef87f25885ee7ca499eaba1939512928f65f55302adcba7dd5e573","abstract_canon_sha256":"d18ec83543aa50234259a026facceb3e5ac3b7d3e41c97fe8d03271b59b39641"},"schema_version":"1.0"},"canonical_sha256":"adb3ef8d14eda1c77e5cd65bb310166f40122a38046e19d62e3afe87fdd31317","source":{"kind":"arxiv","id":"1403.6602","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.6602","created_at":"2026-05-18T02:49:46Z"},{"alias_kind":"arxiv_version","alias_value":"1403.6602v2","created_at":"2026-05-18T02:49:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.6602","created_at":"2026-05-18T02:49:46Z"},{"alias_kind":"pith_short_12","alias_value":"VWZ67DIU5WQ4","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VWZ67DIU5WQ4O7S4","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VWZ67DIU","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:VWZ67DIU5WQ4O7S42ZN3GEAWN5","target":"record","payload":{"canonical_record":{"source":{"id":"1403.6602","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-03-26T09:37:30Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"5cc89a8607ef87f25885ee7ca499eaba1939512928f65f55302adcba7dd5e573","abstract_canon_sha256":"d18ec83543aa50234259a026facceb3e5ac3b7d3e41c97fe8d03271b59b39641"},"schema_version":"1.0"},"canonical_sha256":"adb3ef8d14eda1c77e5cd65bb310166f40122a38046e19d62e3afe87fdd31317","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:46.948402Z","signature_b64":"Ur8miMRv70+F4Er01Ry2//1UUxzvck+OEsuhIEH6E3cWZfQUrg6sfE4VEmRbWpFoGKQGz8JWdxZXAhhFR1aECg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"adb3ef8d14eda1c77e5cd65bb310166f40122a38046e19d62e3afe87fdd31317","last_reissued_at":"2026-05-18T02:49:46.948036Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:46.948036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1403.6602","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":"2026-05-18T02:49:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rHV7o2ff64S0REguV9+T4cpv+ATj1AFjeVSvwu2OIAJpx2sF6JHHeTMH/mHf8+41ehkii/UCaSayaRMItg9gAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T11:03:18.586553Z"},"content_sha256":"be2dbcafa179f1cd46a2f275c55c0b92b36f75f545c2907226ad9bc087025568","schema_version":"1.0","event_id":"sha256:be2dbcafa179f1cd46a2f275c55c0b92b36f75f545c2907226ad9bc087025568"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:VWZ67DIU5WQ4O7S42ZN3GEAWN5","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Pivot Sampling in Dual-Pivot Quicksort","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"cs.DS","authors_text":"Markus E. Nebel, Sebastian Wild","submitted_at":"2014-03-26T09:37:30Z","abstract_excerpt":"The new dual-pivot Quicksort by Vladimir Yaroslavskiy - used in Oracle's Java runtime library since version 7 - features intriguing asymmetries in its behavior. They were shown to cause a basic variant of this algorithm to use less comparisons than classic single-pivot Quicksort implementations. In this paper, we extend the analysis to the case where the two pivots are chosen as fixed order statistics of a random sample and give the precise leading term of the average number of comparisons, swaps and executed Java Bytecode instructions. It turns out that - unlike for classic Quicksort, where i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6602","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":"2026-05-18T02:49:46Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"B2o2pCDbkJkT2aIrF0xwGCA7U4ssTh234IDKVJxcIymFhEz2mmYf6WsOlso2lElD3PZ1iy7j63+Gd7vIt9AbBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-30T11:03:18.586923Z"},"content_sha256":"5c37ab16774c46d5e5bb5b462402a172ffe65b98f98c3d6cd8cad0b1129febcb","schema_version":"1.0","event_id":"sha256:5c37ab16774c46d5e5bb5b462402a172ffe65b98f98c3d6cd8cad0b1129febcb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/VWZ67DIU5WQ4O7S42ZN3GEAWN5/bundle.json","state_url":"https://pith.science/pith/VWZ67DIU5WQ4O7S42ZN3GEAWN5/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/VWZ67DIU5WQ4O7S42ZN3GEAWN5/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":"2026-05-30T11:03:18Z","links":{"resolver":"https://pith.science/pith/VWZ67DIU5WQ4O7S42ZN3GEAWN5","bundle":"https://pith.science/pith/VWZ67DIU5WQ4O7S42ZN3GEAWN5/bundle.json","state":"https://pith.science/pith/VWZ67DIU5WQ4O7S42ZN3GEAWN5/state.json","well_known_bundle":"https://pith.science/.well-known/pith/VWZ67DIU5WQ4O7S42ZN3GEAWN5/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:VWZ67DIU5WQ4O7S42ZN3GEAWN5","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":"d18ec83543aa50234259a026facceb3e5ac3b7d3e41c97fe8d03271b59b39641","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-03-26T09:37:30Z","title_canon_sha256":"5cc89a8607ef87f25885ee7ca499eaba1939512928f65f55302adcba7dd5e573"},"schema_version":"1.0","source":{"id":"1403.6602","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1403.6602","created_at":"2026-05-18T02:49:46Z"},{"alias_kind":"arxiv_version","alias_value":"1403.6602v2","created_at":"2026-05-18T02:49:46Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1403.6602","created_at":"2026-05-18T02:49:46Z"},{"alias_kind":"pith_short_12","alias_value":"VWZ67DIU5WQ4","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VWZ67DIU5WQ4O7S4","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VWZ67DIU","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:5c37ab16774c46d5e5bb5b462402a172ffe65b98f98c3d6cd8cad0b1129febcb","target":"graph","created_at":"2026-05-18T02:49:46Z","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 new dual-pivot Quicksort by Vladimir Yaroslavskiy - used in Oracle's Java runtime library since version 7 - features intriguing asymmetries in its behavior. They were shown to cause a basic variant of this algorithm to use less comparisons than classic single-pivot Quicksort implementations. In this paper, we extend the analysis to the case where the two pivots are chosen as fixed order statistics of a random sample and give the precise leading term of the average number of comparisons, swaps and executed Java Bytecode instructions. It turns out that - unlike for classic Quicksort, where i","authors_text":"Markus E. Nebel, Sebastian Wild","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-03-26T09:37:30Z","title":"Pivot Sampling in Dual-Pivot Quicksort"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6602","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:be2dbcafa179f1cd46a2f275c55c0b92b36f75f545c2907226ad9bc087025568","target":"record","created_at":"2026-05-18T02:49:46Z","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":"d18ec83543aa50234259a026facceb3e5ac3b7d3e41c97fe8d03271b59b39641","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-03-26T09:37:30Z","title_canon_sha256":"5cc89a8607ef87f25885ee7ca499eaba1939512928f65f55302adcba7dd5e573"},"schema_version":"1.0","source":{"id":"1403.6602","kind":"arxiv","version":2}},"canonical_sha256":"adb3ef8d14eda1c77e5cd65bb310166f40122a38046e19d62e3afe87fdd31317","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"adb3ef8d14eda1c77e5cd65bb310166f40122a38046e19d62e3afe87fdd31317","first_computed_at":"2026-05-18T02:49:46.948036Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:49:46.948036Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Ur8miMRv70+F4Er01Ry2//1UUxzvck+OEsuhIEH6E3cWZfQUrg6sfE4VEmRbWpFoGKQGz8JWdxZXAhhFR1aECg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:49:46.948402Z","signed_message":"canonical_sha256_bytes"},"source_id":"1403.6602","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:be2dbcafa179f1cd46a2f275c55c0b92b36f75f545c2907226ad9bc087025568","sha256:5c37ab16774c46d5e5bb5b462402a172ffe65b98f98c3d6cd8cad0b1129febcb"],"state_sha256":"434ed6e4548176ba06e406d5376e01b8bfde6e4d4b31a53e01b1e1203ff509ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"28ps7EM41kQSnVOKYqMKMz+dTgT8HY3N0X8IZi/3P6C7kT9PbJ1LVqRfERqRZUyuwpETPy0tdT0EYHpfeDzGAA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-30T11:03:18.589409Z","bundle_sha256":"40d790a40d2676d394fe9ae85354fc08d82e8797e4bcced55eb4f61e20b15bc7"}}