{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:M2N2UXMD2X4DA3KWD2ASVUR7KQ","short_pith_number":"pith:M2N2UXMD","canonical_record":{"source":{"id":"1307.3033","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-07-11T09:46:33Z","cross_cats_sorted":[],"title_canon_sha256":"50851ffc0bdc99e0c1bfbac625a6cfe2fb805d4013633598597c73297af83dea","abstract_canon_sha256":"ce4b7465ef5eb3e44ed74f13688cc2de6d5e419e960d614dd0ed5d172ef70c31"},"schema_version":"1.0"},"canonical_sha256":"669baa5d83d5f8306d561e812ad23f54177dc74464a4e939e59fe66c07217f9e","source":{"kind":"arxiv","id":"1307.3033","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.3033","created_at":"2026-05-18T03:18:41Z"},{"alias_kind":"arxiv_version","alias_value":"1307.3033v1","created_at":"2026-05-18T03:18:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3033","created_at":"2026-05-18T03:18:41Z"},{"alias_kind":"pith_short_12","alias_value":"M2N2UXMD2X4D","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"M2N2UXMD2X4DA3KW","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"M2N2UXMD","created_at":"2026-05-18T12:27:51Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:M2N2UXMD2X4DA3KWD2ASVUR7KQ","target":"record","payload":{"canonical_record":{"source":{"id":"1307.3033","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-07-11T09:46:33Z","cross_cats_sorted":[],"title_canon_sha256":"50851ffc0bdc99e0c1bfbac625a6cfe2fb805d4013633598597c73297af83dea","abstract_canon_sha256":"ce4b7465ef5eb3e44ed74f13688cc2de6d5e419e960d614dd0ed5d172ef70c31"},"schema_version":"1.0"},"canonical_sha256":"669baa5d83d5f8306d561e812ad23f54177dc74464a4e939e59fe66c07217f9e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:18:41.476857Z","signature_b64":"CSI9zM0oij3G9iPSFHTMpy3qJ3p9UeBwxy+Axvgz7ayFPucOcdNM6RJBCNmLUDZRyWxwES+ewOyVyHcBKUW1DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"669baa5d83d5f8306d561e812ad23f54177dc74464a4e939e59fe66c07217f9e","last_reissued_at":"2026-05-18T03:18:41.476175Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:18:41.476175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.3033","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:18:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Le9d97DSAJJWlZlxRmn+NvVDoQCdHCmQsMLFn6KlilwqBGVBLiWSPOwla3jPvOnWoyF21VLBtMw4i4eYANiJBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:17:43.581453Z"},"content_sha256":"072c16bffa2e79605d0980da2a0fe774eb8d97fe62aa74e0c67312790b027347","schema_version":"1.0","event_id":"sha256:072c16bffa2e79605d0980da2a0fe774eb8d97fe62aa74e0c67312790b027347"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:M2N2UXMD2X4DA3KWD2ASVUR7KQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"QuickXsort: Efficient Sorting with n log n - 1.399n +o(n) Comparisons on Average","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Armin Wei{\\ss}, Stefan Edelkamp","submitted_at":"2013-07-11T09:46:33Z","abstract_excerpt":"In this paper we generalize the idea of QuickHeapsort leading to the notion of QuickXsort. Given some external sorting algorithm X, QuickXsort yields an internal sorting algorithm if X satisfies certain natural conditions.\n  With QuickWeakHeapsort and QuickMergesort we present two examples for the QuickXsort-construction. Both are efficient algorithms that incur approximately n log n - 1.26n +o(n) comparisons on the average. A worst case of n log n + O(n) comparisons can be achieved without significantly affecting the average case.\n  Furthermore, we describe an implementation of MergeInsertion"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3033","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T03:18:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wUkY1+VdGfKsH2AzoYfjURm7UV3clN72bXLgpH6qJXwQsh0RJerk7JCnN1/wqJBtot4GE9+6+iQsNXt2UVvAAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T21:17:43.582134Z"},"content_sha256":"b30386af9a5bdce3f3e51151f96720ef7733d88587cea845a0f7eef8241ff945","schema_version":"1.0","event_id":"sha256:b30386af9a5bdce3f3e51151f96720ef7733d88587cea845a0f7eef8241ff945"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/M2N2UXMD2X4DA3KWD2ASVUR7KQ/bundle.json","state_url":"https://pith.science/pith/M2N2UXMD2X4DA3KWD2ASVUR7KQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/M2N2UXMD2X4DA3KWD2ASVUR7KQ/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":"2026-05-26T21:17:43Z","links":{"resolver":"https://pith.science/pith/M2N2UXMD2X4DA3KWD2ASVUR7KQ","bundle":"https://pith.science/pith/M2N2UXMD2X4DA3KWD2ASVUR7KQ/bundle.json","state":"https://pith.science/pith/M2N2UXMD2X4DA3KWD2ASVUR7KQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/M2N2UXMD2X4DA3KWD2ASVUR7KQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:M2N2UXMD2X4DA3KWD2ASVUR7KQ","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":"ce4b7465ef5eb3e44ed74f13688cc2de6d5e419e960d614dd0ed5d172ef70c31","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-07-11T09:46:33Z","title_canon_sha256":"50851ffc0bdc99e0c1bfbac625a6cfe2fb805d4013633598597c73297af83dea"},"schema_version":"1.0","source":{"id":"1307.3033","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.3033","created_at":"2026-05-18T03:18:41Z"},{"alias_kind":"arxiv_version","alias_value":"1307.3033v1","created_at":"2026-05-18T03:18:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3033","created_at":"2026-05-18T03:18:41Z"},{"alias_kind":"pith_short_12","alias_value":"M2N2UXMD2X4D","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"M2N2UXMD2X4DA3KW","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"M2N2UXMD","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:b30386af9a5bdce3f3e51151f96720ef7733d88587cea845a0f7eef8241ff945","target":"graph","created_at":"2026-05-18T03:18:41Z","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":"In this paper we generalize the idea of QuickHeapsort leading to the notion of QuickXsort. Given some external sorting algorithm X, QuickXsort yields an internal sorting algorithm if X satisfies certain natural conditions.\n  With QuickWeakHeapsort and QuickMergesort we present two examples for the QuickXsort-construction. Both are efficient algorithms that incur approximately n log n - 1.26n +o(n) comparisons on the average. A worst case of n log n + O(n) comparisons can be achieved without significantly affecting the average case.\n  Furthermore, we describe an implementation of MergeInsertion","authors_text":"Armin Wei{\\ss}, Stefan Edelkamp","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-07-11T09:46:33Z","title":"QuickXsort: Efficient Sorting with n log n - 1.399n +o(n) Comparisons on Average"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3033","kind":"arxiv","version":1},"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":"sha256:072c16bffa2e79605d0980da2a0fe774eb8d97fe62aa74e0c67312790b027347","target":"record","created_at":"2026-05-18T03:18:41Z","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":"ce4b7465ef5eb3e44ed74f13688cc2de6d5e419e960d614dd0ed5d172ef70c31","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2013-07-11T09:46:33Z","title_canon_sha256":"50851ffc0bdc99e0c1bfbac625a6cfe2fb805d4013633598597c73297af83dea"},"schema_version":"1.0","source":{"id":"1307.3033","kind":"arxiv","version":1}},"canonical_sha256":"669baa5d83d5f8306d561e812ad23f54177dc74464a4e939e59fe66c07217f9e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"669baa5d83d5f8306d561e812ad23f54177dc74464a4e939e59fe66c07217f9e","first_computed_at":"2026-05-18T03:18:41.476175Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:18:41.476175Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CSI9zM0oij3G9iPSFHTMpy3qJ3p9UeBwxy+Axvgz7ayFPucOcdNM6RJBCNmLUDZRyWxwES+ewOyVyHcBKUW1DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:18:41.476857Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.3033","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:072c16bffa2e79605d0980da2a0fe774eb8d97fe62aa74e0c67312790b027347","sha256:b30386af9a5bdce3f3e51151f96720ef7733d88587cea845a0f7eef8241ff945"],"state_sha256":"9fee28f6e0209c2e0a12321b3ac6270c1a64be38010ffbb5ac357903cdb85cb0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9Hw4NJrY0zJaOCBA2L6dpGlfmwa5VJ4oBFkjFw201V1uKysnlzeN6Ew6Pp0jJoJ8GveBhUuZ3rxVOiT/9PnRDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T21:17:43.585467Z","bundle_sha256":"ff1dd157b6b489dd850ea2770d5baa97d9ed430bb6dee1b73ba3f1a331374744"}}