{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:VKBT7ASKJ2VVCGHXHM4MULSWZS","short_pith_number":"pith:VKBT7ASK","schema_version":"1.0","canonical_sha256":"aa833f824a4eab5118f73b38ca2e56ccb3647f5420834b78773dd182ed7af4d2","source":{"kind":"arxiv","id":"1712.09881","version":4},"attestation_state":"computed","paper":{"title":"On the rate of convergence for the length of the longest common subsequences in hidden Markov models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Christian Houdr\\'e, George Kerchev","submitted_at":"2017-12-28T14:55:59Z","abstract_excerpt":"Let $(X, Y) = (X_n, Y_n)_{n \\geq 1}$ be the output process generated by a hidden chain $Z = (Z_n)_{n \\geq 1}$, where $Z$ is a finite state, aperiodic, time homogeneous, and irreducible Markov chain. Let $LC_n$ be the length of the longest common subsequences of $X_1, \\ldots, X_n$ and $Y_1, \\ldots, Y_n$. Under a mixing hypothesis, a rate of convergence result is obtained for $\\mathbb{E}[LC_n]/n$."},"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":"1712.09881","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-12-28T14:55:59Z","cross_cats_sorted":[],"title_canon_sha256":"2e83706ab418f2e291b347619b0108bf02cc770ad17ec32b0e27679117050e4a","abstract_canon_sha256":"ea6ba4f759fcb70b28e8342733c796ae241e009fda11f9f6900e19a34a47bdd5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:49:22.615989Z","signature_b64":"uoV7JXkfv6eoNHA0v1RjnW7iRPlLvvaEA3M7LXRbRZD0CR8J2FfmlUQagM9feg42t7/W7IqlCEtRJhrEMT3mCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"aa833f824a4eab5118f73b38ca2e56ccb3647f5420834b78773dd182ed7af4d2","last_reissued_at":"2026-05-17T23:49:22.615447Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:49:22.615447Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the rate of convergence for the length of the longest common subsequences in hidden Markov models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Christian Houdr\\'e, George Kerchev","submitted_at":"2017-12-28T14:55:59Z","abstract_excerpt":"Let $(X, Y) = (X_n, Y_n)_{n \\geq 1}$ be the output process generated by a hidden chain $Z = (Z_n)_{n \\geq 1}$, where $Z$ is a finite state, aperiodic, time homogeneous, and irreducible Markov chain. Let $LC_n$ be the length of the longest common subsequences of $X_1, \\ldots, X_n$ and $Y_1, \\ldots, Y_n$. Under a mixing hypothesis, a rate of convergence result is obtained for $\\mathbb{E}[LC_n]/n$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.09881","kind":"arxiv","version":4},"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":"1712.09881","created_at":"2026-05-17T23:49:22.615522+00:00"},{"alias_kind":"arxiv_version","alias_value":"1712.09881v4","created_at":"2026-05-17T23:49:22.615522+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.09881","created_at":"2026-05-17T23:49:22.615522+00:00"},{"alias_kind":"pith_short_12","alias_value":"VKBT7ASKJ2VV","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_16","alias_value":"VKBT7ASKJ2VVCGHX","created_at":"2026-05-18T12:31:49.984773+00:00"},{"alias_kind":"pith_short_8","alias_value":"VKBT7ASK","created_at":"2026-05-18T12:31:49.984773+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/VKBT7ASKJ2VVCGHXHM4MULSWZS","json":"https://pith.science/pith/VKBT7ASKJ2VVCGHXHM4MULSWZS.json","graph_json":"https://pith.science/api/pith-number/VKBT7ASKJ2VVCGHXHM4MULSWZS/graph.json","events_json":"https://pith.science/api/pith-number/VKBT7ASKJ2VVCGHXHM4MULSWZS/events.json","paper":"https://pith.science/paper/VKBT7ASK"},"agent_actions":{"view_html":"https://pith.science/pith/VKBT7ASKJ2VVCGHXHM4MULSWZS","download_json":"https://pith.science/pith/VKBT7ASKJ2VVCGHXHM4MULSWZS.json","view_paper":"https://pith.science/paper/VKBT7ASK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1712.09881&json=true","fetch_graph":"https://pith.science/api/pith-number/VKBT7ASKJ2VVCGHXHM4MULSWZS/graph.json","fetch_events":"https://pith.science/api/pith-number/VKBT7ASKJ2VVCGHXHM4MULSWZS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VKBT7ASKJ2VVCGHXHM4MULSWZS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VKBT7ASKJ2VVCGHXHM4MULSWZS/action/storage_attestation","attest_author":"https://pith.science/pith/VKBT7ASKJ2VVCGHXHM4MULSWZS/action/author_attestation","sign_citation":"https://pith.science/pith/VKBT7ASKJ2VVCGHXHM4MULSWZS/action/citation_signature","submit_replication":"https://pith.science/pith/VKBT7ASKJ2VVCGHXHM4MULSWZS/action/replication_record"}},"created_at":"2026-05-17T23:49:22.615522+00:00","updated_at":"2026-05-17T23:49:22.615522+00:00"}