{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:RF3TEO75T7RYWAJR7MJFVCZBYD","short_pith_number":"pith:RF3TEO75","canonical_record":{"source":{"id":"1510.04676","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-10-15T19:30:29Z","cross_cats_sorted":[],"title_canon_sha256":"74a80df506bccea682f65f6cd7064bacd18144199348d4099267bdc4f2955ade","abstract_canon_sha256":"c46a1b64191aa1dd7d2bebe0e5172868472e86b845286f8cd1de552d68dd1e00"},"schema_version":"1.0"},"canonical_sha256":"8977323bfd9fe38b0131fb125a8b21c0cb3dc8bf101e23740a41718fa4ed5446","source":{"kind":"arxiv","id":"1510.04676","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.04676","created_at":"2026-05-18T01:13:16Z"},{"alias_kind":"arxiv_version","alias_value":"1510.04676v3","created_at":"2026-05-18T01:13:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04676","created_at":"2026-05-18T01:13:16Z"},{"alias_kind":"pith_short_12","alias_value":"RF3TEO75T7RY","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RF3TEO75T7RYWAJR","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RF3TEO75","created_at":"2026-05-18T12:29:39Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:RF3TEO75T7RYWAJR7MJFVCZBYD","target":"record","payload":{"canonical_record":{"source":{"id":"1510.04676","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-10-15T19:30:29Z","cross_cats_sorted":[],"title_canon_sha256":"74a80df506bccea682f65f6cd7064bacd18144199348d4099267bdc4f2955ade","abstract_canon_sha256":"c46a1b64191aa1dd7d2bebe0e5172868472e86b845286f8cd1de552d68dd1e00"},"schema_version":"1.0"},"canonical_sha256":"8977323bfd9fe38b0131fb125a8b21c0cb3dc8bf101e23740a41718fa4ed5446","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:16.469723Z","signature_b64":"/D99Dp8kNtzctOkCgOZF8Hfd/gb3lc1H9aG9Nh5UoAYoZWcqw8hnQGtM0kJc9yA9X5ne5Q8x+GE5sJ+qvaX6AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8977323bfd9fe38b0131fb125a8b21c0cb3dc8bf101e23740a41718fa4ed5446","last_reissued_at":"2026-05-18T01:13:16.469271Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:16.469271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.04676","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:13:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"mA/SFHILwkvrXqSRvx282O+8+MpbPwPS8d7QdviaxwETcZZTdyOhOSgresvgF2lEcBWsJcZ9ZpaNlMnvsH0HAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T21:47:29.418513Z"},"content_sha256":"cb8f7db93976e79cb4d2f76856bc664221ea350e034c736fc313414b3a6fd192","schema_version":"1.0","event_id":"sha256:cb8f7db93976e79cb4d2f76856bc664221ea350e034c736fc313414b3a6fd192"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:RF3TEO75T7RYWAJR7MJFVCZBYD","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"How Good is Multi-Pivot Quicksort?","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Martin Aum\\\"uller, Martin Dietzfelbinger, Pascal Klaue","submitted_at":"2015-10-15T19:30:29Z","abstract_excerpt":"Multi-Pivot Quicksort refers to variants of classical quicksort where in the partitioning step $k$ pivots are used to split the input into $k + 1$ segments. For many years, multi-pivot quicksort was regarded as impractical, but in 2009 a 2-pivot approach by Yaroslavskiy, Bentley, and Bloch was chosen as the standard sorting algorithm in Sun's Java 7. In 2014 at ALENEX, Kushagra et al. introduced an even faster algorithm that uses three pivots. This paper studies what possible advantages multi-pivot quicksort might offer in general. The contributions are as follows: Natural comparison-optimal a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04676","kind":"arxiv","version":3},"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":"2026-05-18T01:13:16Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"pzHpq/IbxcIsz1OWv0gmB2nMOvbfEoW6WF5+VeLNR2bRDH/smqRi/sKa7HjmcDVO7KewR/e7ZpNKatNAeF19BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T21:47:29.418852Z"},"content_sha256":"7826498a160259b87bfc980942dadcb1ab5a0a0378f44e836126c2a3bee50d12","schema_version":"1.0","event_id":"sha256:7826498a160259b87bfc980942dadcb1ab5a0a0378f44e836126c2a3bee50d12"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RF3TEO75T7RYWAJR7MJFVCZBYD/bundle.json","state_url":"https://pith.science/pith/RF3TEO75T7RYWAJR7MJFVCZBYD/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RF3TEO75T7RYWAJR7MJFVCZBYD/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":"2026-06-25T21:47:29Z","links":{"resolver":"https://pith.science/pith/RF3TEO75T7RYWAJR7MJFVCZBYD","bundle":"https://pith.science/pith/RF3TEO75T7RYWAJR7MJFVCZBYD/bundle.json","state":"https://pith.science/pith/RF3TEO75T7RYWAJR7MJFVCZBYD/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RF3TEO75T7RYWAJR7MJFVCZBYD/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:RF3TEO75T7RYWAJR7MJFVCZBYD","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":"c46a1b64191aa1dd7d2bebe0e5172868472e86b845286f8cd1de552d68dd1e00","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-10-15T19:30:29Z","title_canon_sha256":"74a80df506bccea682f65f6cd7064bacd18144199348d4099267bdc4f2955ade"},"schema_version":"1.0","source":{"id":"1510.04676","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.04676","created_at":"2026-05-18T01:13:16Z"},{"alias_kind":"arxiv_version","alias_value":"1510.04676v3","created_at":"2026-05-18T01:13:16Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04676","created_at":"2026-05-18T01:13:16Z"},{"alias_kind":"pith_short_12","alias_value":"RF3TEO75T7RY","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_16","alias_value":"RF3TEO75T7RYWAJR","created_at":"2026-05-18T12:29:39Z"},{"alias_kind":"pith_short_8","alias_value":"RF3TEO75","created_at":"2026-05-18T12:29:39Z"}],"graph_snapshots":[{"event_id":"sha256:7826498a160259b87bfc980942dadcb1ab5a0a0378f44e836126c2a3bee50d12","target":"graph","created_at":"2026-05-18T01:13:16Z","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":"Multi-Pivot Quicksort refers to variants of classical quicksort where in the partitioning step $k$ pivots are used to split the input into $k + 1$ segments. For many years, multi-pivot quicksort was regarded as impractical, but in 2009 a 2-pivot approach by Yaroslavskiy, Bentley, and Bloch was chosen as the standard sorting algorithm in Sun's Java 7. In 2014 at ALENEX, Kushagra et al. introduced an even faster algorithm that uses three pivots. This paper studies what possible advantages multi-pivot quicksort might offer in general. The contributions are as follows: Natural comparison-optimal a","authors_text":"Martin Aum\\\"uller, Martin Dietzfelbinger, Pascal Klaue","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-10-15T19:30:29Z","title":"How Good is Multi-Pivot Quicksort?"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04676","kind":"arxiv","version":3},"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:cb8f7db93976e79cb4d2f76856bc664221ea350e034c736fc313414b3a6fd192","target":"record","created_at":"2026-05-18T01:13:16Z","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":"c46a1b64191aa1dd7d2bebe0e5172868472e86b845286f8cd1de552d68dd1e00","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-10-15T19:30:29Z","title_canon_sha256":"74a80df506bccea682f65f6cd7064bacd18144199348d4099267bdc4f2955ade"},"schema_version":"1.0","source":{"id":"1510.04676","kind":"arxiv","version":3}},"canonical_sha256":"8977323bfd9fe38b0131fb125a8b21c0cb3dc8bf101e23740a41718fa4ed5446","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8977323bfd9fe38b0131fb125a8b21c0cb3dc8bf101e23740a41718fa4ed5446","first_computed_at":"2026-05-18T01:13:16.469271Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:16.469271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"/D99Dp8kNtzctOkCgOZF8Hfd/gb3lc1H9aG9Nh5UoAYoZWcqw8hnQGtM0kJc9yA9X5ne5Q8x+GE5sJ+qvaX6AA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:16.469723Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.04676","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb8f7db93976e79cb4d2f76856bc664221ea350e034c736fc313414b3a6fd192","sha256:7826498a160259b87bfc980942dadcb1ab5a0a0378f44e836126c2a3bee50d12"],"state_sha256":"2ca4fd8d4146ec683d4122c340b4a193c139d95f681cf7a8a251dd95fcab3204"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"evuh4X8U/UVzA30tttyxDGAJLnKmspC97o4do8NN+C6MP4MfC6wOWX7ut87v4D3SiSQEyZFEfoI4BoQrVdmaDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T21:47:29.420846Z","bundle_sha256":"4b51fef92dcd9b7a684d855263432bc17c21af8893c8492142ade87b25a47535"}}