{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:HWNFCVTWLE4NY6SFMNN7OJOWZX","short_pith_number":"pith:HWNFCVTW","schema_version":"1.0","canonical_sha256":"3d9a5156765938dc7a45635bf725d6cddeb4a038b8e15f0eec3a3f219639161c","source":{"kind":"arxiv","id":"1512.05699","version":2},"attestation_state":"computed","paper":{"title":"A Central Limit Theorem for the Optimal Alignments Score in Multiple Random Words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Christian Houdr\\'e, Ruoting Gong, \\\"Umit I\\c{s}lak","submitted_at":"2015-12-17T17:59:06Z","abstract_excerpt":"Let $\\mathbf{X}^{(1)}_{n},\\ldots,\\mathbf{X}^{(m)}_{n}$, where $\\mathbf{X}^{(i)}_{n}=(X^{(i)}_{1},\\ldots,X^{(i)}_{n})$, $i=1,\\ldots,m$, be $m$ independent sequences of independent and identically distributed random variables taking their values in a finite alphabet $\\mathcal{A}$. Let the score function $S$, defined on $\\mathcal{A}^{m}$, be non-negative, bounded, permutation-invariant, and satisfy a bounded differences condition. Under a variance lower-bound assumption, a central limit theorem is proved for the optimal alignments score of the $m$ random words."},"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":"1512.05699","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-12-17T17:59:06Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"4bc29660d2af0f36ec54133a9df4ab3f1eee9851249a8f4985826e5be44cdc35","abstract_canon_sha256":"3a65d76f7f11280280785cec9a111e437786e71531db8cae43cfcd57b7e15269"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:19:11.212177Z","signature_b64":"nZXY21nhd4mKEyOIKVq4rUnDnUUp25Tqra9Py0ve5def1zUve2Hubb9WbN6mJ41zlMi7mbmpYZRSEZPH8Q3iBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3d9a5156765938dc7a45635bf725d6cddeb4a038b8e15f0eec3a3f219639161c","last_reissued_at":"2026-05-18T01:19:11.211374Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:19:11.211374Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Central Limit Theorem for the Optimal Alignments Score in Multiple Random Words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Christian Houdr\\'e, Ruoting Gong, \\\"Umit I\\c{s}lak","submitted_at":"2015-12-17T17:59:06Z","abstract_excerpt":"Let $\\mathbf{X}^{(1)}_{n},\\ldots,\\mathbf{X}^{(m)}_{n}$, where $\\mathbf{X}^{(i)}_{n}=(X^{(i)}_{1},\\ldots,X^{(i)}_{n})$, $i=1,\\ldots,m$, be $m$ independent sequences of independent and identically distributed random variables taking their values in a finite alphabet $\\mathcal{A}$. Let the score function $S$, defined on $\\mathcal{A}^{m}$, be non-negative, bounded, permutation-invariant, and satisfy a bounded differences condition. Under a variance lower-bound assumption, a central limit theorem is proved for the optimal alignments score of the $m$ random words."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05699","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1512.05699","created_at":"2026-05-18T01:19:11.211514+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.05699v2","created_at":"2026-05-18T01:19:11.211514+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.05699","created_at":"2026-05-18T01:19:11.211514+00:00"},{"alias_kind":"pith_short_12","alias_value":"HWNFCVTWLE4N","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_16","alias_value":"HWNFCVTWLE4NY6SF","created_at":"2026-05-18T12:29:25.134429+00:00"},{"alias_kind":"pith_short_8","alias_value":"HWNFCVTW","created_at":"2026-05-18T12:29:25.134429+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/HWNFCVTWLE4NY6SFMNN7OJOWZX","json":"https://pith.science/pith/HWNFCVTWLE4NY6SFMNN7OJOWZX.json","graph_json":"https://pith.science/api/pith-number/HWNFCVTWLE4NY6SFMNN7OJOWZX/graph.json","events_json":"https://pith.science/api/pith-number/HWNFCVTWLE4NY6SFMNN7OJOWZX/events.json","paper":"https://pith.science/paper/HWNFCVTW"},"agent_actions":{"view_html":"https://pith.science/pith/HWNFCVTWLE4NY6SFMNN7OJOWZX","download_json":"https://pith.science/pith/HWNFCVTWLE4NY6SFMNN7OJOWZX.json","view_paper":"https://pith.science/paper/HWNFCVTW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.05699&json=true","fetch_graph":"https://pith.science/api/pith-number/HWNFCVTWLE4NY6SFMNN7OJOWZX/graph.json","fetch_events":"https://pith.science/api/pith-number/HWNFCVTWLE4NY6SFMNN7OJOWZX/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/HWNFCVTWLE4NY6SFMNN7OJOWZX/action/timestamp_anchor","attest_storage":"https://pith.science/pith/HWNFCVTWLE4NY6SFMNN7OJOWZX/action/storage_attestation","attest_author":"https://pith.science/pith/HWNFCVTWLE4NY6SFMNN7OJOWZX/action/author_attestation","sign_citation":"https://pith.science/pith/HWNFCVTWLE4NY6SFMNN7OJOWZX/action/citation_signature","submit_replication":"https://pith.science/pith/HWNFCVTWLE4NY6SFMNN7OJOWZX/action/replication_record"}},"created_at":"2026-05-18T01:19:11.211514+00:00","updated_at":"2026-05-18T01:19:11.211514+00:00"}