{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:TEEPYQCBIYDUBY46NVCLYXBBTD","short_pith_number":"pith:TEEPYQCB","schema_version":"1.0","canonical_sha256":"9908fc4041460740e39e6d44bc5c2198d0ebd365419afe6e0bf24f6b80d84e49","source":{"kind":"arxiv","id":"1102.1842","version":6},"attestation_state":"computed","paper":{"title":"Central limit theorem for Markov processes with spectral gap in the Wasserstein metric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anna Walczuk, Tomasz Komorowski","submitted_at":"2011-02-09T11:46:54Z","abstract_excerpt":"Suppose that $\\{X_t,\\,t\\ge0\\}$ is a non-stationary Markov process, taking values in a Polish metric space $E$. We prove the law of large numbers and central limit theorem for an additive functional of the form $\\int_0^T\\psi(X_s)ds$, provided that the dual transition probability semigroup, defined on measures, is strongly contractive in an appropriate Wasserstein metric. Function $\\psi$ is assumed to be Lipschitz on $E$."},"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":"1102.1842","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-02-09T11:46:54Z","cross_cats_sorted":[],"title_canon_sha256":"4500ee9764313fdb1322705ae6da79ba1b9fca6658b4d241fb5f488b1d717d75","abstract_canon_sha256":"8fbfd67614e3f5e6f9be4af9aa7d47460ab256ceb9ebe85dae149ba117ddc5e2"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:27.542488Z","signature_b64":"C60TDUegDKN1CmmWBctcwb2ibDvQToroPnCPUuFU/5Aoicg48VFRfbYY3803z2ZpTYw3qD2dft3OnkdN6jz4Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9908fc4041460740e39e6d44bc5c2198d0ebd365419afe6e0bf24f6b80d84e49","last_reissued_at":"2026-05-18T03:59:27.541331Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:27.541331Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Central limit theorem for Markov processes with spectral gap in the Wasserstein metric","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anna Walczuk, Tomasz Komorowski","submitted_at":"2011-02-09T11:46:54Z","abstract_excerpt":"Suppose that $\\{X_t,\\,t\\ge0\\}$ is a non-stationary Markov process, taking values in a Polish metric space $E$. We prove the law of large numbers and central limit theorem for an additive functional of the form $\\int_0^T\\psi(X_s)ds$, provided that the dual transition probability semigroup, defined on measures, is strongly contractive in an appropriate Wasserstein metric. Function $\\psi$ is assumed to be Lipschitz on $E$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.1842","kind":"arxiv","version":6},"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":"1102.1842","created_at":"2026-05-18T03:59:27.541442+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.1842v6","created_at":"2026-05-18T03:59:27.541442+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.1842","created_at":"2026-05-18T03:59:27.541442+00:00"},{"alias_kind":"pith_short_12","alias_value":"TEEPYQCBIYDU","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_16","alias_value":"TEEPYQCBIYDUBY46","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_8","alias_value":"TEEPYQCB","created_at":"2026-05-18T12:26:42.757692+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/TEEPYQCBIYDUBY46NVCLYXBBTD","json":"https://pith.science/pith/TEEPYQCBIYDUBY46NVCLYXBBTD.json","graph_json":"https://pith.science/api/pith-number/TEEPYQCBIYDUBY46NVCLYXBBTD/graph.json","events_json":"https://pith.science/api/pith-number/TEEPYQCBIYDUBY46NVCLYXBBTD/events.json","paper":"https://pith.science/paper/TEEPYQCB"},"agent_actions":{"view_html":"https://pith.science/pith/TEEPYQCBIYDUBY46NVCLYXBBTD","download_json":"https://pith.science/pith/TEEPYQCBIYDUBY46NVCLYXBBTD.json","view_paper":"https://pith.science/paper/TEEPYQCB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.1842&json=true","fetch_graph":"https://pith.science/api/pith-number/TEEPYQCBIYDUBY46NVCLYXBBTD/graph.json","fetch_events":"https://pith.science/api/pith-number/TEEPYQCBIYDUBY46NVCLYXBBTD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TEEPYQCBIYDUBY46NVCLYXBBTD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TEEPYQCBIYDUBY46NVCLYXBBTD/action/storage_attestation","attest_author":"https://pith.science/pith/TEEPYQCBIYDUBY46NVCLYXBBTD/action/author_attestation","sign_citation":"https://pith.science/pith/TEEPYQCBIYDUBY46NVCLYXBBTD/action/citation_signature","submit_replication":"https://pith.science/pith/TEEPYQCBIYDUBY46NVCLYXBBTD/action/replication_record"}},"created_at":"2026-05-18T03:59:27.541442+00:00","updated_at":"2026-05-18T03:59:27.541442+00:00"}