{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:BZBVCR5NCR7ESAS2B6F557GVFD","short_pith_number":"pith:BZBVCR5N","schema_version":"1.0","canonical_sha256":"0e435147ad147e49025a0f8bdefcd528fe549e6587454cfe5e86fdfcad04f024","source":{"kind":"arxiv","id":"1702.07691","version":2},"attestation_state":"computed","paper":{"title":"An Almost Sure Invariance Principle for Several Classes of Random Dynamical Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jason Atnip","submitted_at":"2017-02-24T18:20:28Z","abstract_excerpt":"In this paper we deal with a large class of dynamical systems having a version of the spectral gap property. Our primary class of systems comes from random dynamics, but we also deal with the deterministic case. We show that if a random dynamical system has a fiberwise spectral gap property as well as an exponential decay of correlations in the base, then, developing on Gou\\\"{e}zel's approach, the system satisfies the almost sure invariance principle. The result is then applied to uniformly expanding random systems like those studied by Denker and Gordin and Mayer, Skorulski, and Urba\\'nski."},"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":"1702.07691","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-02-24T18:20:28Z","cross_cats_sorted":[],"title_canon_sha256":"1ac05f134117a3e98217e70a7ef4456821c8ae0c6b07c0a84bc15b6582cce590","abstract_canon_sha256":"2ef204c0eb07163b156c5199f6f7f6d88f940908f18714025cc5e78e24b1f5ac"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:23:45.907638Z","signature_b64":"OufDQDOilymyg8CqSCyLheD1Sg3Rln58OLMr8QPPryKqb5ar16w3L2hzZueKoI75jwYgAylPZH9FTI8edEdzCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0e435147ad147e49025a0f8bdefcd528fe549e6587454cfe5e86fdfcad04f024","last_reissued_at":"2026-05-18T00:23:45.907117Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:23:45.907117Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"An Almost Sure Invariance Principle for Several Classes of Random Dynamical Systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jason Atnip","submitted_at":"2017-02-24T18:20:28Z","abstract_excerpt":"In this paper we deal with a large class of dynamical systems having a version of the spectral gap property. Our primary class of systems comes from random dynamics, but we also deal with the deterministic case. We show that if a random dynamical system has a fiberwise spectral gap property as well as an exponential decay of correlations in the base, then, developing on Gou\\\"{e}zel's approach, the system satisfies the almost sure invariance principle. The result is then applied to uniformly expanding random systems like those studied by Denker and Gordin and Mayer, Skorulski, and Urba\\'nski."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.07691","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":"1702.07691","created_at":"2026-05-18T00:23:45.907191+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.07691v2","created_at":"2026-05-18T00:23:45.907191+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.07691","created_at":"2026-05-18T00:23:45.907191+00:00"},{"alias_kind":"pith_short_12","alias_value":"BZBVCR5NCR7E","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_16","alias_value":"BZBVCR5NCR7ESAS2","created_at":"2026-05-18T12:31:08.081275+00:00"},{"alias_kind":"pith_short_8","alias_value":"BZBVCR5N","created_at":"2026-05-18T12:31:08.081275+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/BZBVCR5NCR7ESAS2B6F557GVFD","json":"https://pith.science/pith/BZBVCR5NCR7ESAS2B6F557GVFD.json","graph_json":"https://pith.science/api/pith-number/BZBVCR5NCR7ESAS2B6F557GVFD/graph.json","events_json":"https://pith.science/api/pith-number/BZBVCR5NCR7ESAS2B6F557GVFD/events.json","paper":"https://pith.science/paper/BZBVCR5N"},"agent_actions":{"view_html":"https://pith.science/pith/BZBVCR5NCR7ESAS2B6F557GVFD","download_json":"https://pith.science/pith/BZBVCR5NCR7ESAS2B6F557GVFD.json","view_paper":"https://pith.science/paper/BZBVCR5N","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.07691&json=true","fetch_graph":"https://pith.science/api/pith-number/BZBVCR5NCR7ESAS2B6F557GVFD/graph.json","fetch_events":"https://pith.science/api/pith-number/BZBVCR5NCR7ESAS2B6F557GVFD/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/BZBVCR5NCR7ESAS2B6F557GVFD/action/timestamp_anchor","attest_storage":"https://pith.science/pith/BZBVCR5NCR7ESAS2B6F557GVFD/action/storage_attestation","attest_author":"https://pith.science/pith/BZBVCR5NCR7ESAS2B6F557GVFD/action/author_attestation","sign_citation":"https://pith.science/pith/BZBVCR5NCR7ESAS2B6F557GVFD/action/citation_signature","submit_replication":"https://pith.science/pith/BZBVCR5NCR7ESAS2B6F557GVFD/action/replication_record"}},"created_at":"2026-05-18T00:23:45.907191+00:00","updated_at":"2026-05-18T00:23:45.907191+00:00"}