{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:ZXTQPCHNHNK2VI2VO7LXT6GMQN","short_pith_number":"pith:ZXTQPCHN","schema_version":"1.0","canonical_sha256":"cde70788ed3b55aaa35577d779f8cc8358d63487448aeb5a725612a3982fb469","source":{"kind":"arxiv","id":"1702.01461","version":1},"attestation_state":"computed","paper":{"title":"A note on the finite-dimensional distributions of dispersing billiard processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"math.DS","authors_text":"Juho Lepp\\\"anen, Mikko Stenlund","submitted_at":"2017-02-05T22:41:15Z","abstract_excerpt":"In this short note we consider the finite-dimensional distributions of sets of states generated by dispersing billiards with a random initial condition. We establish a functional correlation bound on the distance between the finite-dimensional distributions and corresponding product distributions. We demonstrate the usefulness of the bound by showing that it implies several limit theorems. The purpose of this note is to provide a tool facilitating the study of more general functionals of the billiard process."},"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":"1702.01461","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-02-05T22:41:15Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"9f333f948a55c539c1155582410fd23b744a68d3a2feb43a5bfaab8f284cf66e","abstract_canon_sha256":"443d3aae7f8b07af58826adaccd8c2496cf9c9162345222715e0957346d250f4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:46:00.393067Z","signature_b64":"lbszH3jUZKIVsBEIAmMyaB/qCXOgWaG7CuiPTLBxZsyV+eDYZFXLVttuTaRiOuvpksfjUjtSHLfCuDyI2goUCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cde70788ed3b55aaa35577d779f8cc8358d63487448aeb5a725612a3982fb469","last_reissued_at":"2026-05-18T00:46:00.392581Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:46:00.392581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A note on the finite-dimensional distributions of dispersing billiard processes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"math.DS","authors_text":"Juho Lepp\\\"anen, Mikko Stenlund","submitted_at":"2017-02-05T22:41:15Z","abstract_excerpt":"In this short note we consider the finite-dimensional distributions of sets of states generated by dispersing billiards with a random initial condition. We establish a functional correlation bound on the distance between the finite-dimensional distributions and corresponding product distributions. We demonstrate the usefulness of the bound by showing that it implies several limit theorems. The purpose of this note is to provide a tool facilitating the study of more general functionals of the billiard process."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01461","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":"1702.01461","created_at":"2026-05-18T00:46:00.392651+00:00"},{"alias_kind":"arxiv_version","alias_value":"1702.01461v1","created_at":"2026-05-18T00:46:00.392651+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.01461","created_at":"2026-05-18T00:46:00.392651+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZXTQPCHNHNK2","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZXTQPCHNHNK2VI2V","created_at":"2026-05-18T12:31:59.375834+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZXTQPCHN","created_at":"2026-05-18T12:31:59.375834+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/ZXTQPCHNHNK2VI2VO7LXT6GMQN","json":"https://pith.science/pith/ZXTQPCHNHNK2VI2VO7LXT6GMQN.json","graph_json":"https://pith.science/api/pith-number/ZXTQPCHNHNK2VI2VO7LXT6GMQN/graph.json","events_json":"https://pith.science/api/pith-number/ZXTQPCHNHNK2VI2VO7LXT6GMQN/events.json","paper":"https://pith.science/paper/ZXTQPCHN"},"agent_actions":{"view_html":"https://pith.science/pith/ZXTQPCHNHNK2VI2VO7LXT6GMQN","download_json":"https://pith.science/pith/ZXTQPCHNHNK2VI2VO7LXT6GMQN.json","view_paper":"https://pith.science/paper/ZXTQPCHN","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1702.01461&json=true","fetch_graph":"https://pith.science/api/pith-number/ZXTQPCHNHNK2VI2VO7LXT6GMQN/graph.json","fetch_events":"https://pith.science/api/pith-number/ZXTQPCHNHNK2VI2VO7LXT6GMQN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZXTQPCHNHNK2VI2VO7LXT6GMQN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZXTQPCHNHNK2VI2VO7LXT6GMQN/action/storage_attestation","attest_author":"https://pith.science/pith/ZXTQPCHNHNK2VI2VO7LXT6GMQN/action/author_attestation","sign_citation":"https://pith.science/pith/ZXTQPCHNHNK2VI2VO7LXT6GMQN/action/citation_signature","submit_replication":"https://pith.science/pith/ZXTQPCHNHNK2VI2VO7LXT6GMQN/action/replication_record"}},"created_at":"2026-05-18T00:46:00.392651+00:00","updated_at":"2026-05-18T00:46:00.392651+00:00"}