{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:QLIQLUCRQSI6Z7ZOM3FBKXF5OR","short_pith_number":"pith:QLIQLUCR","schema_version":"1.0","canonical_sha256":"82d105d0518491ecff2e66ca155cbd746afffd233ed41f0e303d14d28cebe68f","source":{"kind":"arxiv","id":"1407.3377","version":1},"attestation_state":"computed","paper":{"title":"Strengthened Lazy Heaps: Surpassing the Lower Bounds for Binary Heaps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Amr Elmasry, Jyrki Katajainen, Stefan Edelkamp","submitted_at":"2014-07-12T11:50:48Z","abstract_excerpt":"Let $n$ denote the number of elements currently in a data structure. An in-place heap is stored in the first $n$ locations of an array, uses $O(1)$ extra space, and supports the operations: minimum, insert, and extract-min. We introduce an in-place heap, for which minimum and insert take $O(1)$ worst-case time, and extract-min takes $O(\\lg{} n)$ worst-case time and involves at most $\\lg{} n + O(1)$ element comparisons. The achieved bounds are optimal to within additive constant terms for the number of element comparisons. In particular, these bounds for both insert and extract-min -and the tim"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1407.3377","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-07-12T11:50:48Z","cross_cats_sorted":[],"title_canon_sha256":"82a1f755a3f5e391f6ff7d9f0554d5385ce9885e26fc56d8c99a05e27fe03503","abstract_canon_sha256":"3d6676389222ba8cae574e55af93e788fac8152fa2309cf436d65e6425673283"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:43.099734Z","signature_b64":"3GZdMwt5XxFTDEuLA27sgAuKZXhHk8DVS8DlqQ87qQyhkLeLSlRlnr0BT7qWsaQln6SSeY69CKstktPpxetiDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82d105d0518491ecff2e66ca155cbd746afffd233ed41f0e303d14d28cebe68f","last_reissued_at":"2026-05-18T02:47:43.099144Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:43.099144Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strengthened Lazy Heaps: Surpassing the Lower Bounds for Binary Heaps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Amr Elmasry, Jyrki Katajainen, Stefan Edelkamp","submitted_at":"2014-07-12T11:50:48Z","abstract_excerpt":"Let $n$ denote the number of elements currently in a data structure. An in-place heap is stored in the first $n$ locations of an array, uses $O(1)$ extra space, and supports the operations: minimum, insert, and extract-min. We introduce an in-place heap, for which minimum and insert take $O(1)$ worst-case time, and extract-min takes $O(\\lg{} n)$ worst-case time and involves at most $\\lg{} n + O(1)$ element comparisons. The achieved bounds are optimal to within additive constant terms for the number of element comparisons. In particular, these bounds for both insert and extract-min -and the tim"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3377","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1407.3377","created_at":"2026-05-18T02:47:43.099236+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.3377v1","created_at":"2026-05-18T02:47:43.099236+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.3377","created_at":"2026-05-18T02:47:43.099236+00:00"},{"alias_kind":"pith_short_12","alias_value":"QLIQLUCRQSI6","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_16","alias_value":"QLIQLUCRQSI6Z7ZO","created_at":"2026-05-18T12:28:46.137349+00:00"},{"alias_kind":"pith_short_8","alias_value":"QLIQLUCR","created_at":"2026-05-18T12:28:46.137349+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/QLIQLUCRQSI6Z7ZOM3FBKXF5OR","json":"https://pith.science/pith/QLIQLUCRQSI6Z7ZOM3FBKXF5OR.json","graph_json":"https://pith.science/api/pith-number/QLIQLUCRQSI6Z7ZOM3FBKXF5OR/graph.json","events_json":"https://pith.science/api/pith-number/QLIQLUCRQSI6Z7ZOM3FBKXF5OR/events.json","paper":"https://pith.science/paper/QLIQLUCR"},"agent_actions":{"view_html":"https://pith.science/pith/QLIQLUCRQSI6Z7ZOM3FBKXF5OR","download_json":"https://pith.science/pith/QLIQLUCRQSI6Z7ZOM3FBKXF5OR.json","view_paper":"https://pith.science/paper/QLIQLUCR","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.3377&json=true","fetch_graph":"https://pith.science/api/pith-number/QLIQLUCRQSI6Z7ZOM3FBKXF5OR/graph.json","fetch_events":"https://pith.science/api/pith-number/QLIQLUCRQSI6Z7ZOM3FBKXF5OR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/QLIQLUCRQSI6Z7ZOM3FBKXF5OR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/QLIQLUCRQSI6Z7ZOM3FBKXF5OR/action/storage_attestation","attest_author":"https://pith.science/pith/QLIQLUCRQSI6Z7ZOM3FBKXF5OR/action/author_attestation","sign_citation":"https://pith.science/pith/QLIQLUCRQSI6Z7ZOM3FBKXF5OR/action/citation_signature","submit_replication":"https://pith.science/pith/QLIQLUCRQSI6Z7ZOM3FBKXF5OR/action/replication_record"}},"created_at":"2026-05-18T02:47:43.099236+00:00","updated_at":"2026-05-18T02:47:43.099236+00:00"}