{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:XUATG32FNR3H475SIMZHICRTA4","short_pith_number":"pith:XUATG32F","schema_version":"1.0","canonical_sha256":"bd01336f456c767e7fb24332740a33072ff4e39d4ac25dd3f83cc4d11cec0ef2","source":{"kind":"arxiv","id":"1904.05459","version":2},"attestation_state":"computed","paper":{"title":"Constant factor approximations to edit distance on far input pairs in nearly linear time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Michael E. Saks, Michal Kouck\\'y","submitted_at":"2019-04-10T21:52:07Z","abstract_excerpt":"For any $T \\geq 1$, there are constants $R=R(T) \\geq 1$ and $\\zeta=\\zeta(T)>0$ and a randomized algorithm that takes as input an integer $n$ and two strings $x,y$ of length at most $n$, and runs in time $O(n^{1+\\frac{1}{T}})$ and outputs an upper bound $U$ on the edit distance $ED(x,y)$ that with high probability, satisfies $U \\leq R(ED(x,y)+n^{1-\\zeta})$. In particular, on any input with $ED(x,y) \\geq n^{1-\\zeta}$ the algorithm outputs a constant factor approximation with high probability.\n  A similar result has been proven independently by Brakensiek and Rubinstein (2019)."},"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":"1904.05459","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-04-10T21:52:07Z","cross_cats_sorted":[],"title_canon_sha256":"1afc9a03200bc03033fb56a8c402c158c200daeb38be837598956ac7b8c9e521","abstract_canon_sha256":"1d842fecce112ba45c72c96e0d8e07ac6f774086e1583ce52287623460b3ab97"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:46:40.826271Z","signature_b64":"n24Uu63ALdeP0z301jHnNgjxgvuc/e5fQkGo5GRmkQ5pndei1+mMDq+zj4EtRxOW4OU4GvGvVoEulht1LNS8Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"bd01336f456c767e7fb24332740a33072ff4e39d4ac25dd3f83cc4d11cec0ef2","last_reissued_at":"2026-05-17T23:46:40.825416Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:46:40.825416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Constant factor approximations to edit distance on far input pairs in nearly linear time","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Michael E. Saks, Michal Kouck\\'y","submitted_at":"2019-04-10T21:52:07Z","abstract_excerpt":"For any $T \\geq 1$, there are constants $R=R(T) \\geq 1$ and $\\zeta=\\zeta(T)>0$ and a randomized algorithm that takes as input an integer $n$ and two strings $x,y$ of length at most $n$, and runs in time $O(n^{1+\\frac{1}{T}})$ and outputs an upper bound $U$ on the edit distance $ED(x,y)$ that with high probability, satisfies $U \\leq R(ED(x,y)+n^{1-\\zeta})$. In particular, on any input with $ED(x,y) \\geq n^{1-\\zeta}$ the algorithm outputs a constant factor approximation with high probability.\n  A similar result has been proven independently by Brakensiek and Rubinstein (2019)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.05459","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1904.05459","created_at":"2026-05-17T23:46:40.825581+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.05459v2","created_at":"2026-05-17T23:46:40.825581+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.05459","created_at":"2026-05-17T23:46:40.825581+00:00"},{"alias_kind":"pith_short_12","alias_value":"XUATG32FNR3H","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_16","alias_value":"XUATG32FNR3H475S","created_at":"2026-05-18T12:33:33.725879+00:00"},{"alias_kind":"pith_short_8","alias_value":"XUATG32F","created_at":"2026-05-18T12:33:33.725879+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/XUATG32FNR3H475SIMZHICRTA4","json":"https://pith.science/pith/XUATG32FNR3H475SIMZHICRTA4.json","graph_json":"https://pith.science/api/pith-number/XUATG32FNR3H475SIMZHICRTA4/graph.json","events_json":"https://pith.science/api/pith-number/XUATG32FNR3H475SIMZHICRTA4/events.json","paper":"https://pith.science/paper/XUATG32F"},"agent_actions":{"view_html":"https://pith.science/pith/XUATG32FNR3H475SIMZHICRTA4","download_json":"https://pith.science/pith/XUATG32FNR3H475SIMZHICRTA4.json","view_paper":"https://pith.science/paper/XUATG32F","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.05459&json=true","fetch_graph":"https://pith.science/api/pith-number/XUATG32FNR3H475SIMZHICRTA4/graph.json","fetch_events":"https://pith.science/api/pith-number/XUATG32FNR3H475SIMZHICRTA4/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/XUATG32FNR3H475SIMZHICRTA4/action/timestamp_anchor","attest_storage":"https://pith.science/pith/XUATG32FNR3H475SIMZHICRTA4/action/storage_attestation","attest_author":"https://pith.science/pith/XUATG32FNR3H475SIMZHICRTA4/action/author_attestation","sign_citation":"https://pith.science/pith/XUATG32FNR3H475SIMZHICRTA4/action/citation_signature","submit_replication":"https://pith.science/pith/XUATG32FNR3H475SIMZHICRTA4/action/replication_record"}},"created_at":"2026-05-17T23:46:40.825581+00:00","updated_at":"2026-05-17T23:46:40.825581+00:00"}