{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:XUATG32FNR3H475SIMZHICRTA4","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":"1d842fecce112ba45c72c96e0d8e07ac6f774086e1583ce52287623460b3ab97","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-04-10T21:52:07Z","title_canon_sha256":"1afc9a03200bc03033fb56a8c402c158c200daeb38be837598956ac7b8c9e521"},"schema_version":"1.0","source":{"id":"1904.05459","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1904.05459","created_at":"2026-05-17T23:46:40Z"},{"alias_kind":"arxiv_version","alias_value":"1904.05459v2","created_at":"2026-05-17T23:46:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.05459","created_at":"2026-05-17T23:46:40Z"},{"alias_kind":"pith_short_12","alias_value":"XUATG32FNR3H","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_16","alias_value":"XUATG32FNR3H475S","created_at":"2026-05-18T12:33:33Z"},{"alias_kind":"pith_short_8","alias_value":"XUATG32F","created_at":"2026-05-18T12:33:33Z"}],"graph_snapshots":[{"event_id":"sha256:5352b8bcf3cccd3d65cadd0b6573539d6fac8deeb1bc0f73d01c18fe267e67a0","target":"graph","created_at":"2026-05-17T23:46:40Z","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":"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).","authors_text":"Michael E. Saks, Michal Kouck\\'y","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-04-10T21:52:07Z","title":"Constant factor approximations to edit distance on far input pairs in nearly linear time"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.05459","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":"sha256:032d973315ae9e34c97ffa40d7457adc8eb99648cc6f29cf67da223003ab0b6e","target":"record","created_at":"2026-05-17T23:46:40Z","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":"1d842fecce112ba45c72c96e0d8e07ac6f774086e1583ce52287623460b3ab97","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2019-04-10T21:52:07Z","title_canon_sha256":"1afc9a03200bc03033fb56a8c402c158c200daeb38be837598956ac7b8c9e521"},"schema_version":"1.0","source":{"id":"1904.05459","kind":"arxiv","version":2}},"canonical_sha256":"bd01336f456c767e7fb24332740a33072ff4e39d4ac25dd3f83cc4d11cec0ef2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"bd01336f456c767e7fb24332740a33072ff4e39d4ac25dd3f83cc4d11cec0ef2","first_computed_at":"2026-05-17T23:46:40.825416Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:46:40.825416Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n24Uu63ALdeP0z301jHnNgjxgvuc/e5fQkGo5GRmkQ5pndei1+mMDq+zj4EtRxOW4OU4GvGvVoEulht1LNS8Aw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:46:40.826271Z","signed_message":"canonical_sha256_bytes"},"source_id":"1904.05459","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:032d973315ae9e34c97ffa40d7457adc8eb99648cc6f29cf67da223003ab0b6e","sha256:5352b8bcf3cccd3d65cadd0b6573539d6fac8deeb1bc0f73d01c18fe267e67a0"],"state_sha256":"3a57c19cf3abd8cac12d97b9b9c0eb42366ad798f5e46bd4db5356feaa5f685e"}