{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:5AV6MXNSJD7OTQ253VURCH5J3W","short_pith_number":"pith:5AV6MXNS","schema_version":"1.0","canonical_sha256":"e82be65db248fee9c35ddd69111fa9dda13e28ef171fb80abddf094e053f620e","source":{"kind":"arxiv","id":"2504.10425","version":1},"attestation_state":"computed","paper":{"title":"Expected Length of the Longest Common Subsequence of Multiple Strings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.PR"],"primary_cat":"math.CO","authors_text":"Ray Li, William Ren, Yiran Wen","submitted_at":"2025-04-14T17:15:51Z","abstract_excerpt":"We study the generalized Chv\\'atal-Sankoff constant $\\gamma_{k,d}$, which represents the normalized expected length of the longest common subsequence (LCS) of $d$ independent uniformly random strings over an alphabet of size $k$. We derive asymptotically tight bounds for $\\gamma_{2,d}$, establishing that $\\gamma_{2,d} = \\frac{1}{2} + \\Theta\\left(\\frac{1}{\\sqrt{d}}\\right)$. We also derive asymptotically near-optimal bounds on $\\gamma_{k,d}$ for $d\\ge \\Omega(\\log k)$."},"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":"2504.10425","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CO","submitted_at":"2025-04-14T17:15:51Z","cross_cats_sorted":["cs.DM","math.PR"],"title_canon_sha256":"218485b590c267bbbed1ded26638e22d350eb5b26670b3f1524f7ca353b5ad98","abstract_canon_sha256":"dd919e4a3662710aa1357f3616724c069c2fa5abd9bb66b459c101d8cf22c83e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T10:49:00.135816Z","signature_b64":"pmyovDXDtqmK8SjeOL+ZnIP5eZdJbbmJEGf3FWGTfbXRr9/7PQbGw8o6OcX6qh95UiadtS1KigLfkNzgZ5MhCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e82be65db248fee9c35ddd69111fa9dda13e28ef171fb80abddf094e053f620e","last_reissued_at":"2026-07-05T10:49:00.135320Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T10:49:00.135320Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Expected Length of the Longest Common Subsequence of Multiple Strings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.DM","math.PR"],"primary_cat":"math.CO","authors_text":"Ray Li, William Ren, Yiran Wen","submitted_at":"2025-04-14T17:15:51Z","abstract_excerpt":"We study the generalized Chv\\'atal-Sankoff constant $\\gamma_{k,d}$, which represents the normalized expected length of the longest common subsequence (LCS) of $d$ independent uniformly random strings over an alphabet of size $k$. We derive asymptotically tight bounds for $\\gamma_{2,d}$, establishing that $\\gamma_{2,d} = \\frac{1}{2} + \\Theta\\left(\\frac{1}{\\sqrt{d}}\\right)$. We also derive asymptotically near-optimal bounds on $\\gamma_{k,d}$ for $d\\ge \\Omega(\\log k)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.10425","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2504.10425/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2504.10425","created_at":"2026-07-05T10:49:00.135378+00:00"},{"alias_kind":"arxiv_version","alias_value":"2504.10425v1","created_at":"2026-07-05T10:49:00.135378+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2504.10425","created_at":"2026-07-05T10:49:00.135378+00:00"},{"alias_kind":"pith_short_12","alias_value":"5AV6MXNSJD7O","created_at":"2026-07-05T10:49:00.135378+00:00"},{"alias_kind":"pith_short_16","alias_value":"5AV6MXNSJD7OTQ25","created_at":"2026-07-05T10:49:00.135378+00:00"},{"alias_kind":"pith_short_8","alias_value":"5AV6MXNS","created_at":"2026-07-05T10:49:00.135378+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/5AV6MXNSJD7OTQ253VURCH5J3W","json":"https://pith.science/pith/5AV6MXNSJD7OTQ253VURCH5J3W.json","graph_json":"https://pith.science/api/pith-number/5AV6MXNSJD7OTQ253VURCH5J3W/graph.json","events_json":"https://pith.science/api/pith-number/5AV6MXNSJD7OTQ253VURCH5J3W/events.json","paper":"https://pith.science/paper/5AV6MXNS"},"agent_actions":{"view_html":"https://pith.science/pith/5AV6MXNSJD7OTQ253VURCH5J3W","download_json":"https://pith.science/pith/5AV6MXNSJD7OTQ253VURCH5J3W.json","view_paper":"https://pith.science/paper/5AV6MXNS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2504.10425&json=true","fetch_graph":"https://pith.science/api/pith-number/5AV6MXNSJD7OTQ253VURCH5J3W/graph.json","fetch_events":"https://pith.science/api/pith-number/5AV6MXNSJD7OTQ253VURCH5J3W/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/5AV6MXNSJD7OTQ253VURCH5J3W/action/timestamp_anchor","attest_storage":"https://pith.science/pith/5AV6MXNSJD7OTQ253VURCH5J3W/action/storage_attestation","attest_author":"https://pith.science/pith/5AV6MXNSJD7OTQ253VURCH5J3W/action/author_attestation","sign_citation":"https://pith.science/pith/5AV6MXNSJD7OTQ253VURCH5J3W/action/citation_signature","submit_replication":"https://pith.science/pith/5AV6MXNSJD7OTQ253VURCH5J3W/action/replication_record"}},"created_at":"2026-07-05T10:49:00.135378+00:00","updated_at":"2026-07-05T10:49:00.135378+00:00"}