{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:AIIYTVH4OQG4XZTK3AGFKWKAYO","short_pith_number":"pith:AIIYTVH4","canonical_record":{"source":{"id":"1704.01311","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-04-05T08:45:22Z","cross_cats_sorted":[],"title_canon_sha256":"ac19df0eb54e5869ffeaf1327b7f366eb41e69004aafccffe3413f918153517f","abstract_canon_sha256":"1974c40aa71d81dd44e1eb980b1f3c1178f641f0be4be48e7a57b306f48e6613"},"schema_version":"1.0"},"canonical_sha256":"021189d4fc740dcbe66ad80c555940c391e33efc9457ea6823e05f571aeecbce","source":{"kind":"arxiv","id":"1704.01311","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.01311","created_at":"2026-05-18T00:46:58Z"},{"alias_kind":"arxiv_version","alias_value":"1704.01311v1","created_at":"2026-05-18T00:46:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.01311","created_at":"2026-05-18T00:46:58Z"},{"alias_kind":"pith_short_12","alias_value":"AIIYTVH4OQG4","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"AIIYTVH4OQG4XZTK","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"AIIYTVH4","created_at":"2026-05-18T12:31:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:AIIYTVH4OQG4XZTK3AGFKWKAYO","target":"record","payload":{"canonical_record":{"source":{"id":"1704.01311","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-04-05T08:45:22Z","cross_cats_sorted":[],"title_canon_sha256":"ac19df0eb54e5869ffeaf1327b7f366eb41e69004aafccffe3413f918153517f","abstract_canon_sha256":"1974c40aa71d81dd44e1eb980b1f3c1178f641f0be4be48e7a57b306f48e6613"},"schema_version":"1.0"},"canonical_sha256":"021189d4fc740dcbe66ad80c555940c391e33efc9457ea6823e05f571aeecbce","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:58.487224Z","signature_b64":"NJ+/KqLOQ83EV8/3cppsOT4pixI07XhjlF0pC5tiV/jUgrMLHu1J4K1GkEtglQ5Yj+cCQHQbyjhHKCB3BA6lCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"021189d4fc740dcbe66ad80c555940c391e33efc9457ea6823e05f571aeecbce","last_reissued_at":"2026-05-18T00:46:58.486733Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:58.486733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1704.01311","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":"2026-05-18T00:46:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vRWpDgqgE4MonTXYDX3pZbBLO5FSKPABRYWx4/B2vwYP59gsn0/cMedKoRA+k2C3aPNCVSAh3CjWoph0w/l+BQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:03:26.612415Z"},"content_sha256":"91da93d65e40611b92ea56c05b1d2f928f8476bcd76e2bce531ad293a9c47d8b","schema_version":"1.0","event_id":"sha256:91da93d65e40611b92ea56c05b1d2f928f8476bcd76e2bce531ad293a9c47d8b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:AIIYTVH4OQG4XZTK3AGFKWKAYO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Optimal trade-offs for pattern matching with $k$ mismatches","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Pawe{\\l} Gawrychowski, Przemys{\\l}aw Uzna\\'nski","submitted_at":"2017-04-05T08:45:22Z","abstract_excerpt":"Given a pattern of length $m$ and a text of length $n$, the goal in $k$-mismatch pattern matching is to compute, for every $m$-substring of the text, the exact Hamming distance to the pattern or report that it exceeds $k$. This can be solved in either $\\widetilde{O}(n \\sqrt{k})$ time as shown by Amir et al. [J. Algorithms 2004] or $\\widetilde{O}((m + k^2) \\cdot n/m)$ time due to a result of Clifford et al. [SODA 2016]. We provide a smooth time trade-off between these two bounds by designing an algorithm working in time $\\widetilde{O}( (m + k \\sqrt{m}) \\cdot n/m)$. We complement this with a mat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01311","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":"2026-05-18T00:46:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YaSWycbkd1xkZo7YAWoynCYQPkG+mNbYtq9yQmJxe+0Z3XDwG9kaHEAjvM35hiUnaD06+lydyH5xvTLkexVJCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-09T07:03:26.613182Z"},"content_sha256":"3352a7f19e542f387f01b5bac3c49c80e66a46a5f728d94104ebe97bc1884b7a","schema_version":"1.0","event_id":"sha256:3352a7f19e542f387f01b5bac3c49c80e66a46a5f728d94104ebe97bc1884b7a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AIIYTVH4OQG4XZTK3AGFKWKAYO/bundle.json","state_url":"https://pith.science/pith/AIIYTVH4OQG4XZTK3AGFKWKAYO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AIIYTVH4OQG4XZTK3AGFKWKAYO/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":"2026-06-09T07:03:26Z","links":{"resolver":"https://pith.science/pith/AIIYTVH4OQG4XZTK3AGFKWKAYO","bundle":"https://pith.science/pith/AIIYTVH4OQG4XZTK3AGFKWKAYO/bundle.json","state":"https://pith.science/pith/AIIYTVH4OQG4XZTK3AGFKWKAYO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AIIYTVH4OQG4XZTK3AGFKWKAYO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:AIIYTVH4OQG4XZTK3AGFKWKAYO","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":"1974c40aa71d81dd44e1eb980b1f3c1178f641f0be4be48e7a57b306f48e6613","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-04-05T08:45:22Z","title_canon_sha256":"ac19df0eb54e5869ffeaf1327b7f366eb41e69004aafccffe3413f918153517f"},"schema_version":"1.0","source":{"id":"1704.01311","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1704.01311","created_at":"2026-05-18T00:46:58Z"},{"alias_kind":"arxiv_version","alias_value":"1704.01311v1","created_at":"2026-05-18T00:46:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.01311","created_at":"2026-05-18T00:46:58Z"},{"alias_kind":"pith_short_12","alias_value":"AIIYTVH4OQG4","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"AIIYTVH4OQG4XZTK","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"AIIYTVH4","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:3352a7f19e542f387f01b5bac3c49c80e66a46a5f728d94104ebe97bc1884b7a","target":"graph","created_at":"2026-05-18T00:46:58Z","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":"Given a pattern of length $m$ and a text of length $n$, the goal in $k$-mismatch pattern matching is to compute, for every $m$-substring of the text, the exact Hamming distance to the pattern or report that it exceeds $k$. This can be solved in either $\\widetilde{O}(n \\sqrt{k})$ time as shown by Amir et al. [J. Algorithms 2004] or $\\widetilde{O}((m + k^2) \\cdot n/m)$ time due to a result of Clifford et al. [SODA 2016]. We provide a smooth time trade-off between these two bounds by designing an algorithm working in time $\\widetilde{O}( (m + k \\sqrt{m}) \\cdot n/m)$. We complement this with a mat","authors_text":"Pawe{\\l} Gawrychowski, Przemys{\\l}aw Uzna\\'nski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-04-05T08:45:22Z","title":"Optimal trade-offs for pattern matching with $k$ mismatches"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.01311","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":"sha256:91da93d65e40611b92ea56c05b1d2f928f8476bcd76e2bce531ad293a9c47d8b","target":"record","created_at":"2026-05-18T00:46:58Z","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":"1974c40aa71d81dd44e1eb980b1f3c1178f641f0be4be48e7a57b306f48e6613","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2017-04-05T08:45:22Z","title_canon_sha256":"ac19df0eb54e5869ffeaf1327b7f366eb41e69004aafccffe3413f918153517f"},"schema_version":"1.0","source":{"id":"1704.01311","kind":"arxiv","version":1}},"canonical_sha256":"021189d4fc740dcbe66ad80c555940c391e33efc9457ea6823e05f571aeecbce","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"021189d4fc740dcbe66ad80c555940c391e33efc9457ea6823e05f571aeecbce","first_computed_at":"2026-05-18T00:46:58.486733Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:58.486733Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"NJ+/KqLOQ83EV8/3cppsOT4pixI07XhjlF0pC5tiV/jUgrMLHu1J4K1GkEtglQ5Yj+cCQHQbyjhHKCB3BA6lCA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:58.487224Z","signed_message":"canonical_sha256_bytes"},"source_id":"1704.01311","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:91da93d65e40611b92ea56c05b1d2f928f8476bcd76e2bce531ad293a9c47d8b","sha256:3352a7f19e542f387f01b5bac3c49c80e66a46a5f728d94104ebe97bc1884b7a"],"state_sha256":"bba04cdf966d161c91191a67bd3f1c33648c6eb3701d6bd8f622a65fb1fb880c"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fQGV255MXXRpePsk9CpShh/WO7LppeInmYLupwcRU/b5P5x12hpsU3pCcI1oI1WxZ5gZZ/1+nokrEHaqmGFCAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-09T07:03:26.617602Z","bundle_sha256":"41125df04d594de7716b92cb86cf7364710e6d4c2f11663a91e32920401ac8bf"}}