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We provide \"quenched\" large deviation estimates for the random family of measures $q^\\epsilon_1(x)dx$: there exists a continuous, explicit mapping $\\bar J : R^2\\to R$ such that for almost all $B_\\cdot,V_\\cdot$, $\\bar J(\\cdot,X_1)$ is a good rate function and for any measurable $G\\subset R$, $$-\\inf_{x\\in G^o} \\bar J(x,X_1) \\leq \\liminf \\"},"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":"math/0306020","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2003-06-01T14:06:46Z","cross_cats_sorted":[],"title_canon_sha256":"9078bf670fe658aa3719eb9811a430f0a6a444b8eb7dead79005b7865f038fc9","abstract_canon_sha256":"b912aa4c0bf7d2f08112adfbf69d8b52d49ad78c0e358fab02b9815078784888"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:49:20.769595Z","signature_b64":"F86cSPtqG/79Cni5/CTALxtAvf/yy2yxDykjoFN9CJyNwCsp7NBgW4oShF/FRSIcbhZ3I0J9twfBPqcbm6kgAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9d5d2908e6a01f19f526a664a49b0fab9abf31d0cbb0f035018a4a2c0b0ec345","last_reissued_at":"2026-05-18T02:49:20.768979Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:49:20.768979Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Quenched large deviations for one dimensional nonlinear filtering","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"E. 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We provide \"quenched\" large deviation estimates for the random family of measures $q^\\epsilon_1(x)dx$: there exists a continuous, explicit mapping $\\bar J : R^2\\to R$ such that for almost all $B_\\cdot,V_\\cdot$, $\\bar J(\\cdot,X_1)$ is a good rate function and for any measurable $G\\subset R$, $$-\\inf_{x\\in G^o} \\bar J(x,X_1) \\leq \\liminf \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0306020","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":"math/0306020","created_at":"2026-05-18T02:49:20.769062+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0306020v2","created_at":"2026-05-18T02:49:20.769062+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0306020","created_at":"2026-05-18T02:49:20.769062+00:00"},{"alias_kind":"pith_short_12","alias_value":"TVOSSCHGUAPR","created_at":"2026-05-18T12:25:52.051335+00:00"},{"alias_kind":"pith_short_16","alias_value":"TVOSSCHGUAPRT5JG","created_at":"2026-05-18T12:25:52.051335+00:00"},{"alias_kind":"pith_short_8","alias_value":"TVOSSCHG","created_at":"2026-05-18T12:25:52.051335+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/TVOSSCHGUAPRT5JGUZSKJGYPVO","json":"https://pith.science/pith/TVOSSCHGUAPRT5JGUZSKJGYPVO.json","graph_json":"https://pith.science/api/pith-number/TVOSSCHGUAPRT5JGUZSKJGYPVO/graph.json","events_json":"https://pith.science/api/pith-number/TVOSSCHGUAPRT5JGUZSKJGYPVO/events.json","paper":"https://pith.science/paper/TVOSSCHG"},"agent_actions":{"view_html":"https://pith.science/pith/TVOSSCHGUAPRT5JGUZSKJGYPVO","download_json":"https://pith.science/pith/TVOSSCHGUAPRT5JGUZSKJGYPVO.json","view_paper":"https://pith.science/paper/TVOSSCHG","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0306020&json=true","fetch_graph":"https://pith.science/api/pith-number/TVOSSCHGUAPRT5JGUZSKJGYPVO/graph.json","fetch_events":"https://pith.science/api/pith-number/TVOSSCHGUAPRT5JGUZSKJGYPVO/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TVOSSCHGUAPRT5JGUZSKJGYPVO/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TVOSSCHGUAPRT5JGUZSKJGYPVO/action/storage_attestation","attest_author":"https://pith.science/pith/TVOSSCHGUAPRT5JGUZSKJGYPVO/action/author_attestation","sign_citation":"https://pith.science/pith/TVOSSCHGUAPRT5JGUZSKJGYPVO/action/citation_signature","submit_replication":"https://pith.science/pith/TVOSSCHGUAPRT5JGUZSKJGYPVO/action/replication_record"}},"created_at":"2026-05-18T02:49:20.769062+00:00","updated_at":"2026-05-18T02:49:20.769062+00:00"}