{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:AORILNJLMFRBGS6QKRIEAY5YSS","short_pith_number":"pith:AORILNJL","canonical_record":{"source":{"id":"1409.1694","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-09-05T08:57:02Z","cross_cats_sorted":[],"title_canon_sha256":"98c1a9de5b33cec8c53a0dc6d373d8e6989309fd8931c9a8a319658c4b9d20f6","abstract_canon_sha256":"d57c34142b9cda52b3ac21535c2b6d81c13d5da3edc66cca33e6d0b534f388dd"},"schema_version":"1.0"},"canonical_sha256":"03a285b52b6162134bd054504063b89496846e68c0b8fccc9d5d67985850c2bb","source":{"kind":"arxiv","id":"1409.1694","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.1694","created_at":"2026-05-18T02:19:28Z"},{"alias_kind":"arxiv_version","alias_value":"1409.1694v2","created_at":"2026-05-18T02:19:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.1694","created_at":"2026-05-18T02:19:28Z"},{"alias_kind":"pith_short_12","alias_value":"AORILNJLMFRB","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AORILNJLMFRBGS6Q","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AORILNJL","created_at":"2026-05-18T12:28:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:AORILNJLMFRBGS6QKRIEAY5YSS","target":"record","payload":{"canonical_record":{"source":{"id":"1409.1694","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-09-05T08:57:02Z","cross_cats_sorted":[],"title_canon_sha256":"98c1a9de5b33cec8c53a0dc6d373d8e6989309fd8931c9a8a319658c4b9d20f6","abstract_canon_sha256":"d57c34142b9cda52b3ac21535c2b6d81c13d5da3edc66cca33e6d0b534f388dd"},"schema_version":"1.0"},"canonical_sha256":"03a285b52b6162134bd054504063b89496846e68c0b8fccc9d5d67985850c2bb","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:19:28.333664Z","signature_b64":"OWsXITxQjjCr6r2yLFRhkmEMisXvjdhOar2FibHyP5/5fzucd8B1w2Y6dOOwgrwXeBwbpsDoImI/R9P+zk6DDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03a285b52b6162134bd054504063b89496846e68c0b8fccc9d5d67985850c2bb","last_reissued_at":"2026-05-18T02:19:28.333027Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:19:28.333027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1409.1694","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:19:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ROsjRo59Dmgb7w340q7gKGbLbYWueR6/elfNT0Fb13aKtt5kpgTKfa4kHaGMMgROHDDIh0TVBR+wC55zxwNiAQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T10:32:39.554860Z"},"content_sha256":"71815ffd34d758fe2a83a4a20a17b68453d87a5509b66470d9532d1e07d979d7","schema_version":"1.0","event_id":"sha256:71815ffd34d758fe2a83a4a20a17b68453d87a5509b66470d9532d1e07d979d7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:AORILNJLMFRBGS6QKRIEAY5YSS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Longest common substrings with k mismatches","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"cs.DS","authors_text":"Emanuele Giaquinta, Esko Ukkonen, Kassian Kobert, Tomas Flouri","submitted_at":"2014-09-05T08:57:02Z","abstract_excerpt":"The longest common substring with $k$-mismatches problem is to find, given two strings $S_1$ and $S_2$, a longest substring $A_1$ of $S_1$ and $A_2$ of $S_2$ such that the Hamming distance between $A_1$ and $A_2$ is $\\le k$. We introduce a practical $O(nm)$ time and $O(1)$ space solution for this problem, where $n$ and $m$ are the lengths of $S_1$ and $S_2$, respectively. This algorithm can also be used to compute the matching statistics with $k$-mismatches of $S_1$ and $S_2$ in $O(nm)$ time and $O(m)$ space. Moreover, we also present a theoretical solution for the $k = 1$ case which runs in $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1694","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:19:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h/VRo7oHPU/M2L39Wd/0qyvNQla0TTBZm3TiXpfc0g+A/DFhjIkmv8bf640dlSQChI23L0nh1Cd+j56aB8zwDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-22T10:32:39.555209Z"},"content_sha256":"18f4ab865955a35c7b76f11f969468e045343f9197e3def79d62e41156920e70","schema_version":"1.0","event_id":"sha256:18f4ab865955a35c7b76f11f969468e045343f9197e3def79d62e41156920e70"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/AORILNJLMFRBGS6QKRIEAY5YSS/bundle.json","state_url":"https://pith.science/pith/AORILNJLMFRBGS6QKRIEAY5YSS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/AORILNJLMFRBGS6QKRIEAY5YSS/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":"2026-06-22T10:32:39Z","links":{"resolver":"https://pith.science/pith/AORILNJLMFRBGS6QKRIEAY5YSS","bundle":"https://pith.science/pith/AORILNJLMFRBGS6QKRIEAY5YSS/bundle.json","state":"https://pith.science/pith/AORILNJLMFRBGS6QKRIEAY5YSS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/AORILNJLMFRBGS6QKRIEAY5YSS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:AORILNJLMFRBGS6QKRIEAY5YSS","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":"d57c34142b9cda52b3ac21535c2b6d81c13d5da3edc66cca33e6d0b534f388dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-09-05T08:57:02Z","title_canon_sha256":"98c1a9de5b33cec8c53a0dc6d373d8e6989309fd8931c9a8a319658c4b9d20f6"},"schema_version":"1.0","source":{"id":"1409.1694","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.1694","created_at":"2026-05-18T02:19:28Z"},{"alias_kind":"arxiv_version","alias_value":"1409.1694v2","created_at":"2026-05-18T02:19:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.1694","created_at":"2026-05-18T02:19:28Z"},{"alias_kind":"pith_short_12","alias_value":"AORILNJLMFRB","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_16","alias_value":"AORILNJLMFRBGS6Q","created_at":"2026-05-18T12:28:19Z"},{"alias_kind":"pith_short_8","alias_value":"AORILNJL","created_at":"2026-05-18T12:28:19Z"}],"graph_snapshots":[{"event_id":"sha256:18f4ab865955a35c7b76f11f969468e045343f9197e3def79d62e41156920e70","target":"graph","created_at":"2026-05-18T02:19:28Z","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 longest common substring with $k$-mismatches problem is to find, given two strings $S_1$ and $S_2$, a longest substring $A_1$ of $S_1$ and $A_2$ of $S_2$ such that the Hamming distance between $A_1$ and $A_2$ is $\\le k$. We introduce a practical $O(nm)$ time and $O(1)$ space solution for this problem, where $n$ and $m$ are the lengths of $S_1$ and $S_2$, respectively. This algorithm can also be used to compute the matching statistics with $k$-mismatches of $S_1$ and $S_2$ in $O(nm)$ time and $O(m)$ space. Moreover, we also present a theoretical solution for the $k = 1$ case which runs in $","authors_text":"Emanuele Giaquinta, Esko Ukkonen, Kassian Kobert, Tomas Flouri","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-09-05T08:57:02Z","title":"Longest common substrings with k mismatches"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.1694","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":"sha256:71815ffd34d758fe2a83a4a20a17b68453d87a5509b66470d9532d1e07d979d7","target":"record","created_at":"2026-05-18T02:19:28Z","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":"d57c34142b9cda52b3ac21535c2b6d81c13d5da3edc66cca33e6d0b534f388dd","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cs.DS","submitted_at":"2014-09-05T08:57:02Z","title_canon_sha256":"98c1a9de5b33cec8c53a0dc6d373d8e6989309fd8931c9a8a319658c4b9d20f6"},"schema_version":"1.0","source":{"id":"1409.1694","kind":"arxiv","version":2}},"canonical_sha256":"03a285b52b6162134bd054504063b89496846e68c0b8fccc9d5d67985850c2bb","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03a285b52b6162134bd054504063b89496846e68c0b8fccc9d5d67985850c2bb","first_computed_at":"2026-05-18T02:19:28.333027Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:19:28.333027Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OWsXITxQjjCr6r2yLFRhkmEMisXvjdhOar2FibHyP5/5fzucd8B1w2Y6dOOwgrwXeBwbpsDoImI/R9P+zk6DDw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:19:28.333664Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.1694","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:71815ffd34d758fe2a83a4a20a17b68453d87a5509b66470d9532d1e07d979d7","sha256:18f4ab865955a35c7b76f11f969468e045343f9197e3def79d62e41156920e70"],"state_sha256":"68dfb2e2720af62b104b8489331e2902d8253dc1d879d35759b1f0bef26ba97a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"HuNti4lgJV6g9Bsz8TgNd/NGXZtzPE2zmbGGGzVsX0cq5CSJxKUKUF3ONAmauYaVoVqPZteSgtHKG+iGIhdqDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-22T10:32:39.557184Z","bundle_sha256":"b598bd82e9b1ad9f0165e0ef35de830ff449bcc894ea1fa33b602fa743515f5c"}}