{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:P4AFMYCXIFXTXDXMJQFR3P3IFI","short_pith_number":"pith:P4AFMYCX","schema_version":"1.0","canonical_sha256":"7f00566057416f3b8eec4c0b1dbf682a37ebdad55443f39ed9635962da8e4e12","source":{"kind":"arxiv","id":"1210.0902","version":3},"attestation_state":"computed","paper":{"title":"A vector-valued almost sure invariance principle for Sinai billiards with random scatterers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"math.DS","authors_text":"Mikko Stenlund","submitted_at":"2012-10-02T20:00:01Z","abstract_excerpt":"Understanding the statistical properties of the aperiodic planar Lorentz gas stands as a grand challenge in the theory of dynamical systems. Here we study a greatly simplified but related model, proposed by Arvind Ayyer and popularized by Joel Lebowitz, in which a scatterer configuration on the torus is randomly updated between collisions. Taking advantage of recent progress in the theory of time-dependent billiards on the one hand and in probability theory on the other, we prove a vector-valued almost sure invariance principle for the model. Notably, the configuration sequence can be weakly d"},"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":"1210.0902","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2012-10-02T20:00:01Z","cross_cats_sorted":["math-ph","math.MP","math.PR"],"title_canon_sha256":"444d946901353e65d1837eec8795a3c7db4d013cf29f33350d6e49b5782cfc56","abstract_canon_sha256":"05bd4b230dd020185f4e1bced42bc9b624b15cb74bbb21a342779dbf6f4ac8f0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:10.547567Z","signature_b64":"5uueBi3K8gbzWbDmHbg2WwnxgD+/QWbbrl6rAWZU3OvR2G9S7g72/99xtP3FWumFBA+Tr7kGyf17I6ryBFe0AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f00566057416f3b8eec4c0b1dbf682a37ebdad55443f39ed9635962da8e4e12","last_reissued_at":"2026-05-18T03:21:10.546943Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:10.546943Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A vector-valued almost sure invariance principle for Sinai billiards with random scatterers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","math.PR"],"primary_cat":"math.DS","authors_text":"Mikko Stenlund","submitted_at":"2012-10-02T20:00:01Z","abstract_excerpt":"Understanding the statistical properties of the aperiodic planar Lorentz gas stands as a grand challenge in the theory of dynamical systems. Here we study a greatly simplified but related model, proposed by Arvind Ayyer and popularized by Joel Lebowitz, in which a scatterer configuration on the torus is randomly updated between collisions. Taking advantage of recent progress in the theory of time-dependent billiards on the one hand and in probability theory on the other, we prove a vector-valued almost sure invariance principle for the model. Notably, the configuration sequence can be weakly d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1210.0902","kind":"arxiv","version":3},"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":"1210.0902","created_at":"2026-05-18T03:21:10.547041+00:00"},{"alias_kind":"arxiv_version","alias_value":"1210.0902v3","created_at":"2026-05-18T03:21:10.547041+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1210.0902","created_at":"2026-05-18T03:21:10.547041+00:00"},{"alias_kind":"pith_short_12","alias_value":"P4AFMYCXIFXT","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_16","alias_value":"P4AFMYCXIFXTXDXM","created_at":"2026-05-18T12:27:18.751474+00:00"},{"alias_kind":"pith_short_8","alias_value":"P4AFMYCX","created_at":"2026-05-18T12:27:18.751474+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/P4AFMYCXIFXTXDXMJQFR3P3IFI","json":"https://pith.science/pith/P4AFMYCXIFXTXDXMJQFR3P3IFI.json","graph_json":"https://pith.science/api/pith-number/P4AFMYCXIFXTXDXMJQFR3P3IFI/graph.json","events_json":"https://pith.science/api/pith-number/P4AFMYCXIFXTXDXMJQFR3P3IFI/events.json","paper":"https://pith.science/paper/P4AFMYCX"},"agent_actions":{"view_html":"https://pith.science/pith/P4AFMYCXIFXTXDXMJQFR3P3IFI","download_json":"https://pith.science/pith/P4AFMYCXIFXTXDXMJQFR3P3IFI.json","view_paper":"https://pith.science/paper/P4AFMYCX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1210.0902&json=true","fetch_graph":"https://pith.science/api/pith-number/P4AFMYCXIFXTXDXMJQFR3P3IFI/graph.json","fetch_events":"https://pith.science/api/pith-number/P4AFMYCXIFXTXDXMJQFR3P3IFI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P4AFMYCXIFXTXDXMJQFR3P3IFI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P4AFMYCXIFXTXDXMJQFR3P3IFI/action/storage_attestation","attest_author":"https://pith.science/pith/P4AFMYCXIFXTXDXMJQFR3P3IFI/action/author_attestation","sign_citation":"https://pith.science/pith/P4AFMYCXIFXTXDXMJQFR3P3IFI/action/citation_signature","submit_replication":"https://pith.science/pith/P4AFMYCXIFXTXDXMJQFR3P3IFI/action/replication_record"}},"created_at":"2026-05-18T03:21:10.547041+00:00","updated_at":"2026-05-18T03:21:10.547041+00:00"}