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Let LCI$_n$ be the length of the longest common and (weakly) increasing subsequence of $X_1\\cdots X_n$ and $Y_1\\cdots Y_n$. As $n$ grows without bound, and when properly centered and normalized, LCI$_n$ is shown to converge, in distribution, towards a Brownian functional that we identify."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1505.06164","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-05-22T18:00:24Z","cross_cats_sorted":[],"title_canon_sha256":"20c6b499db34793a3cb27d20880745c4936ed9c0c34183a8fe14c7547a3e882c","abstract_canon_sha256":"67710fb6abb13a5769c69ac1b4db958661cf2aa57871030ecee6fda80830afc8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:07:24.024577Z","signature_b64":"HS6tJyjwiKuKVs8zQG5EZmXW3H2bDVTRUM9DbjKEc3eCxYx+mZpAkHQiT2jlK6/uxh77oe7Mw9nOd/6P341wAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"18e0c7b23d21cac09993b3733573ff2e2d5b6875a337378ee523b8049ee74359","last_reissued_at":"2026-05-18T00:07:24.024158Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:07:24.024158Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the limiting law of the length of the longest common and increasing subsequences in random words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Christian Houdr\\'e, Jean-Christophe Breton","submitted_at":"2015-05-22T18:00:24Z","abstract_excerpt":"Let $X=(X_i)_{i\\ge 1}$ and $Y=(Y_i)_{i\\ge 1}$ be two sequences of independent and identically distributed (iid) random variables taking their values, uniformly, in a common totally ordered finite alphabet. Let LCI$_n$ be the length of the longest common and (weakly) increasing subsequence of $X_1\\cdots X_n$ and $Y_1\\cdots Y_n$. As $n$ grows without bound, and when properly centered and normalized, LCI$_n$ is shown to converge, in distribution, towards a Brownian functional that we identify."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.06164","kind":"arxiv","version":3},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1505.06164","created_at":"2026-05-18T00:07:24.024226+00:00"},{"alias_kind":"arxiv_version","alias_value":"1505.06164v3","created_at":"2026-05-18T00:07:24.024226+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1505.06164","created_at":"2026-05-18T00:07:24.024226+00:00"},{"alias_kind":"pith_short_12","alias_value":"DDQMPMR5EHFM","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_16","alias_value":"DDQMPMR5EHFMBGMT","created_at":"2026-05-18T12:29:17.054201+00:00"},{"alias_kind":"pith_short_8","alias_value":"DDQMPMR5","created_at":"2026-05-18T12:29:17.054201+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/DDQMPMR5EHFMBGMTWNZTK477FY","json":"https://pith.science/pith/DDQMPMR5EHFMBGMTWNZTK477FY.json","graph_json":"https://pith.science/api/pith-number/DDQMPMR5EHFMBGMTWNZTK477FY/graph.json","events_json":"https://pith.science/api/pith-number/DDQMPMR5EHFMBGMTWNZTK477FY/events.json","paper":"https://pith.science/paper/DDQMPMR5"},"agent_actions":{"view_html":"https://pith.science/pith/DDQMPMR5EHFMBGMTWNZTK477FY","download_json":"https://pith.science/pith/DDQMPMR5EHFMBGMTWNZTK477FY.json","view_paper":"https://pith.science/paper/DDQMPMR5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1505.06164&json=true","fetch_graph":"https://pith.science/api/pith-number/DDQMPMR5EHFMBGMTWNZTK477FY/graph.json","fetch_events":"https://pith.science/api/pith-number/DDQMPMR5EHFMBGMTWNZTK477FY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/DDQMPMR5EHFMBGMTWNZTK477FY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/DDQMPMR5EHFMBGMTWNZTK477FY/action/storage_attestation","attest_author":"https://pith.science/pith/DDQMPMR5EHFMBGMTWNZTK477FY/action/author_attestation","sign_citation":"https://pith.science/pith/DDQMPMR5EHFMBGMTWNZTK477FY/action/citation_signature","submit_replication":"https://pith.science/pith/DDQMPMR5EHFMBGMTWNZTK477FY/action/replication_record"}},"created_at":"2026-05-18T00:07:24.024226+00:00","updated_at":"2026-05-18T00:07:24.024226+00:00"}