{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:YX337UM7EIYFV3OO4PDNRV5BWK","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":"d9a4afb6e566391452fd3008675865f93c0e2dad4582af23c67eae5d79f4508a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-12-14T20:53:15Z","title_canon_sha256":"999080caab497237c9123fe93f211200a277e64225d9c478f1da3dbdaf2587b3"},"schema_version":"1.0","source":{"id":"1512.04515","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.04515","created_at":"2026-05-18T01:24:22Z"},{"alias_kind":"arxiv_version","alias_value":"1512.04515v1","created_at":"2026-05-18T01:24:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.04515","created_at":"2026-05-18T01:24:22Z"},{"alias_kind":"pith_short_12","alias_value":"YX337UM7EIYF","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"YX337UM7EIYFV3OO","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"YX337UM7","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:9bb9dec93264d9c689c35002a871396394a235f6004ae7163d27d8bb3ab901e9","target":"graph","created_at":"2026-05-18T01:24:22Z","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":"The algorithmic tasks of computing the Hamming distance between a given pattern of length $m$ and each location in a text of length $n$ is one of the most fundamental algorithmic tasks in string algorithms. Unfortunately, there is evidence that for a text $T$ of size $n$ and a pattern $P$ of size $m$, one cannot compute the exact Hamming distance for all locations in $T$ in time which is less than $\\tilde O(n\\sqrt m)$. However, Karloff~\\cite{karloff} showed that if one is willing to suffer a $1\\pm\\epsilon$ approximation, then it is possible to solve the problem with high probability, in $\\tild","authors_text":"Ely Porat, Tsvi Kopelowitz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-12-14T20:53:15Z","title":"Breaking the Variance: Approximating the Hamming Distance in $\\tilde O(1/\\epsilon)$ Time Per Alignment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.04515","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":"sha256:8a5ad9a57a515c5417933e6a68378d9c86a184e1ad6afb1c88b2aba4f64089ca","target":"record","created_at":"2026-05-18T01:24:22Z","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":"d9a4afb6e566391452fd3008675865f93c0e2dad4582af23c67eae5d79f4508a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2015-12-14T20:53:15Z","title_canon_sha256":"999080caab497237c9123fe93f211200a277e64225d9c478f1da3dbdaf2587b3"},"schema_version":"1.0","source":{"id":"1512.04515","kind":"arxiv","version":1}},"canonical_sha256":"c5f7bfd19f22305aedcee3c6d8d7a1b2805df606679a725e1cf93aee6a1e9165","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c5f7bfd19f22305aedcee3c6d8d7a1b2805df606679a725e1cf93aee6a1e9165","first_computed_at":"2026-05-18T01:24:22.079308Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:24:22.079308Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"fOgoCFIHBP4iTB8TSyWzef6XljbMSoQqPj2XcsE3NwsOcFM8B1phK0jRxgT/CzpZ3rLWwvtkr6VEcmaYcEcQAA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:24:22.079982Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.04515","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:8a5ad9a57a515c5417933e6a68378d9c86a184e1ad6afb1c88b2aba4f64089ca","sha256:9bb9dec93264d9c689c35002a871396394a235f6004ae7163d27d8bb3ab901e9"],"state_sha256":"361031bea667ce7e594a3a90051e2c2caa1a5ebdb0fa0dd6c4fe0373cb8c7521"}