{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:F4EWMCMZQODXTRKZTTWCRU5ZEK","short_pith_number":"pith:F4EWMCMZ","schema_version":"1.0","canonical_sha256":"2f09660999838779c5599cec28d3b92292be09f0bfe3f5a44a529c966d881ab1","source":{"kind":"arxiv","id":"1310.5451","version":1},"attestation_state":"computed","paper":{"title":"Strong approximation results for the empirical process of stationary sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Emmanuel Rio, Florence Merlev\\`ede, J\\'er\\^ome Dedecker","submitted_at":"2013-10-21T07:56:05Z","abstract_excerpt":"We prove a strong approximation result for the empirical process associated to a stationary sequence of real-valued random variables, under dependence conditions involving only indicators of half lines. This strong approximation result also holds for the empirical process associated to iterates of expanding maps with a neutral fixed point at zero, as soon as the correlations decrease more rapidly than $n^{-1-\\delta}$ for some positive $\\delta$. This shows that our conditions are in some sense optimal."},"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":"1310.5451","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-21T07:56:05Z","cross_cats_sorted":[],"title_canon_sha256":"9e2fc9f06b154a76f018538b1427e718da088da6068ebdb2c0e4285d984d0c2d","abstract_canon_sha256":"ccb99bf1dbf63ba10353eb3f74a9ec50c2bcf66aaaae75fe25a7c4e7984dbdba"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:09:35.624411Z","signature_b64":"I20C+8OJIuyriFkwlTkgAxhja43JtW0CFqy50HlYjyGbU0NuoHjDMNEEuARJv6jooh6QD89ByImEpruI0c/XBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2f09660999838779c5599cec28d3b92292be09f0bfe3f5a44a529c966d881ab1","last_reissued_at":"2026-05-18T03:09:35.623329Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:09:35.623329Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Strong approximation results for the empirical process of stationary sequences","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Emmanuel Rio, Florence Merlev\\`ede, J\\'er\\^ome Dedecker","submitted_at":"2013-10-21T07:56:05Z","abstract_excerpt":"We prove a strong approximation result for the empirical process associated to a stationary sequence of real-valued random variables, under dependence conditions involving only indicators of half lines. This strong approximation result also holds for the empirical process associated to iterates of expanding maps with a neutral fixed point at zero, as soon as the correlations decrease more rapidly than $n^{-1-\\delta}$ for some positive $\\delta$. This shows that our conditions are in some sense optimal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5451","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":""},"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":"1310.5451","created_at":"2026-05-18T03:09:35.623488+00:00"},{"alias_kind":"arxiv_version","alias_value":"1310.5451v1","created_at":"2026-05-18T03:09:35.623488+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.5451","created_at":"2026-05-18T03:09:35.623488+00:00"},{"alias_kind":"pith_short_12","alias_value":"F4EWMCMZQODX","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_16","alias_value":"F4EWMCMZQODXTRKZ","created_at":"2026-05-18T12:27:43.054852+00:00"},{"alias_kind":"pith_short_8","alias_value":"F4EWMCMZ","created_at":"2026-05-18T12:27:43.054852+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/F4EWMCMZQODXTRKZTTWCRU5ZEK","json":"https://pith.science/pith/F4EWMCMZQODXTRKZTTWCRU5ZEK.json","graph_json":"https://pith.science/api/pith-number/F4EWMCMZQODXTRKZTTWCRU5ZEK/graph.json","events_json":"https://pith.science/api/pith-number/F4EWMCMZQODXTRKZTTWCRU5ZEK/events.json","paper":"https://pith.science/paper/F4EWMCMZ"},"agent_actions":{"view_html":"https://pith.science/pith/F4EWMCMZQODXTRKZTTWCRU5ZEK","download_json":"https://pith.science/pith/F4EWMCMZQODXTRKZTTWCRU5ZEK.json","view_paper":"https://pith.science/paper/F4EWMCMZ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1310.5451&json=true","fetch_graph":"https://pith.science/api/pith-number/F4EWMCMZQODXTRKZTTWCRU5ZEK/graph.json","fetch_events":"https://pith.science/api/pith-number/F4EWMCMZQODXTRKZTTWCRU5ZEK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F4EWMCMZQODXTRKZTTWCRU5ZEK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F4EWMCMZQODXTRKZTTWCRU5ZEK/action/storage_attestation","attest_author":"https://pith.science/pith/F4EWMCMZQODXTRKZTTWCRU5ZEK/action/author_attestation","sign_citation":"https://pith.science/pith/F4EWMCMZQODXTRKZTTWCRU5ZEK/action/citation_signature","submit_replication":"https://pith.science/pith/F4EWMCMZQODXTRKZTTWCRU5ZEK/action/replication_record"}},"created_at":"2026-05-18T03:09:35.623488+00:00","updated_at":"2026-05-18T03:09:35.623488+00:00"}