{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:ZXTQPCHNHNK2VI2VO7LXT6GMQN","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"443d3aae7f8b07af58826adaccd8c2496cf9c9162345222715e0957346d250f4","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-02-05T22:41:15Z","title_canon_sha256":"9f333f948a55c539c1155582410fd23b744a68d3a2feb43a5bfaab8f284cf66e"},"schema_version":"1.0","source":{"id":"1702.01461","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1702.01461","created_at":"2026-05-18T00:46:00Z"},{"alias_kind":"arxiv_version","alias_value":"1702.01461v1","created_at":"2026-05-18T00:46:00Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1702.01461","created_at":"2026-05-18T00:46:00Z"},{"alias_kind":"pith_short_12","alias_value":"ZXTQPCHNHNK2","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_16","alias_value":"ZXTQPCHNHNK2VI2V","created_at":"2026-05-18T12:31:59Z"},{"alias_kind":"pith_short_8","alias_value":"ZXTQPCHN","created_at":"2026-05-18T12:31:59Z"}],"graph_snapshots":[{"event_id":"sha256:dea0bfd152bb20c2650709a9a9a167509d834b405b03686d6a8ffb84fb48d143","target":"graph","created_at":"2026-05-18T00:46:00Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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.","authors_text":"Juho Lepp\\\"anen, Mikko Stenlund","cross_cats":["math-ph","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-02-05T22:41:15Z","title":"A note on the finite-dimensional distributions of dispersing billiard processes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01461","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:3872bf3add7e3fe0e7a27a3c881ceba1923ced85cd3a9a71f01d15be4cfaa63d","target":"record","created_at":"2026-05-18T00:46:00Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"443d3aae7f8b07af58826adaccd8c2496cf9c9162345222715e0957346d250f4","cross_cats_sorted":["math-ph","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-02-05T22:41:15Z","title_canon_sha256":"9f333f948a55c539c1155582410fd23b744a68d3a2feb43a5bfaab8f284cf66e"},"schema_version":"1.0","source":{"id":"1702.01461","kind":"arxiv","version":1}},"canonical_sha256":"cde70788ed3b55aaa35577d779f8cc8358d63487448aeb5a725612a3982fb469","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cde70788ed3b55aaa35577d779f8cc8358d63487448aeb5a725612a3982fb469","first_computed_at":"2026-05-18T00:46:00.392581Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:46:00.392581Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"lbszH3jUZKIVsBEIAmMyaB/qCXOgWaG7CuiPTLBxZsyV+eDYZFXLVttuTaRiOuvpksfjUjtSHLfCuDyI2goUCw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:46:00.393067Z","signed_message":"canonical_sha256_bytes"},"source_id":"1702.01461","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3872bf3add7e3fe0e7a27a3c881ceba1923ced85cd3a9a71f01d15be4cfaa63d","sha256:dea0bfd152bb20c2650709a9a9a167509d834b405b03686d6a8ffb84fb48d143"],"state_sha256":"550cce541c879efdd4e27078473a94985fa82d2a39ee4b970a5a73c03bff271f"}