{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:5MAORXPQVJ6BNF4CSST7AOJX3Y","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":"97251b4001dc0ed6103e8b4ec8e41aad1cf849111e29f4856590015d00c772ae","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-01-08T14:06:03Z","title_canon_sha256":"fa84a15fa7fbeb0af1e01c205f96b7415f7717dc94160ed0ce8fdfa5be58401c"},"schema_version":"1.0","source":{"id":"1001.1273","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1001.1273","created_at":"2026-05-18T04:36:08Z"},{"alias_kind":"arxiv_version","alias_value":"1001.1273v3","created_at":"2026-05-18T04:36:08Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1001.1273","created_at":"2026-05-18T04:36:08Z"},{"alias_kind":"pith_short_12","alias_value":"5MAORXPQVJ6B","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_16","alias_value":"5MAORXPQVJ6BNF4C","created_at":"2026-05-18T12:26:04Z"},{"alias_kind":"pith_short_8","alias_value":"5MAORXPQ","created_at":"2026-05-18T12:26:04Z"}],"graph_snapshots":[{"event_id":"sha256:60ca33610ddaf5aec51f8c2a0ac598bf11152fe60664dad892c8aa14a585c0e4","target":"graph","created_at":"2026-05-18T04:36:08Z","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 problem of the fluctuation of the Longest Common Subsequence (LCS) of two i.i.d. sequences of length $n>0$ has been open for decades. There exist contradicting conjectures on the topic. Chvatal and Sankoff conjectured in 1975 that asymptotically the order should be $n^{2/3}$, while Waterman conjectured in 1994 that asymptotically the order should be $n$. A contiguous substring consisting only of one type of symbol is called a block. In the present work, we determine the order of the fluctuation of the LCS for a special model of sequences consisting of i.i.d. blocks whose lengths are unifor","authors_text":"Felipe Torres, Heinrich Matzinger","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-01-08T14:06:03Z","title":"Fluctuations of the Longest Common Subsequence for Sequences of Independent Blocks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1001.1273","kind":"arxiv","version":3},"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":"sha256:6b77fd42a39659f073a3df958eb649d11289fdb344458d0a16941a53f62270cd","target":"record","created_at":"2026-05-18T04:36:08Z","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":"97251b4001dc0ed6103e8b4ec8e41aad1cf849111e29f4856590015d00c772ae","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-01-08T14:06:03Z","title_canon_sha256":"fa84a15fa7fbeb0af1e01c205f96b7415f7717dc94160ed0ce8fdfa5be58401c"},"schema_version":"1.0","source":{"id":"1001.1273","kind":"arxiv","version":3}},"canonical_sha256":"eb00e8ddf0aa7c16978294a7f03937de2d79944a1ca1090a6b87c68329708553","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb00e8ddf0aa7c16978294a7f03937de2d79944a1ca1090a6b87c68329708553","first_computed_at":"2026-05-18T04:36:08.710797Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:36:08.710797Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"GxdeXwTweqz1R1L5w6j61vDzNCAUEt2DiWpSGk3OK4L1rhYLeMkB4vnPNJW8fH/2rTpMfB/1VqrGcybc5BAKDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:36:08.711191Z","signed_message":"canonical_sha256_bytes"},"source_id":"1001.1273","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b77fd42a39659f073a3df958eb649d11289fdb344458d0a16941a53f62270cd","sha256:60ca33610ddaf5aec51f8c2a0ac598bf11152fe60664dad892c8aa14a585c0e4"],"state_sha256":"ee305efba5298f7f7ec4b35e750874d36f0b17f58d7113e3615730105bd5ebe5"}