{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:3RNNNCAWNY56L44X4U5YOZW24Q","short_pith_number":"pith:3RNNNCAW","schema_version":"1.0","canonical_sha256":"dc5ad688166e3be5f397e53b8766dae400722678115cf395cedf80dc24659277","source":{"kind":"arxiv","id":"1404.5661","version":1},"attestation_state":"computed","paper":{"title":"A Sampling Theorem for Rotation Numbers of Linear Processes in ${\\R}^{2}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.DS","authors_text":"Paulo R. C. Ruffino","submitted_at":"2014-04-22T21:59:25Z","abstract_excerpt":"We prove an ergodic theorem for the rotation number of the composition of a sequence os stationary random homeomorphisms in $S^{1}$. In particular, the concept of rotation number of a matrix $g\\in Gl^{+}(2,{\\R})$ can be generalized to a product of a sequence of stationary random matrices in $Gl^{+}(2,{\\R})$. In this particular case this result provides a counter-part of the Osseledec's multiplicative ergodic theorem which guarantees the existence of Lyapunov exponents. A random sampling theorem is then proved to show that the concept we propose is consistent by discretization in time with the "},"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":"1404.5661","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-04-22T21:59:25Z","cross_cats_sorted":["math.PR"],"title_canon_sha256":"8080716cb87c1201a53c44b34e7a8938ea29a0e37d80e6fcf523b518abb08913","abstract_canon_sha256":"54f6e2867ca74c331802ba0fe190339643a730bb0f7cd19c48d30295540c85a7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:53:28.226050Z","signature_b64":"bjsGPDcgNPCgZLZr+kN67lDnUR66/c2pBNCH7ibo9/WAMKKuRz8w4qAGhCIJT1Hvx9IP6M5BIwjjHowN2YBUAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dc5ad688166e3be5f397e53b8766dae400722678115cf395cedf80dc24659277","last_reissued_at":"2026-05-18T02:53:28.225399Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:53:28.225399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Sampling Theorem for Rotation Numbers of Linear Processes in ${\\R}^{2}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.DS","authors_text":"Paulo R. C. Ruffino","submitted_at":"2014-04-22T21:59:25Z","abstract_excerpt":"We prove an ergodic theorem for the rotation number of the composition of a sequence os stationary random homeomorphisms in $S^{1}$. In particular, the concept of rotation number of a matrix $g\\in Gl^{+}(2,{\\R})$ can be generalized to a product of a sequence of stationary random matrices in $Gl^{+}(2,{\\R})$. In this particular case this result provides a counter-part of the Osseledec's multiplicative ergodic theorem which guarantees the existence of Lyapunov exponents. A random sampling theorem is then proved to show that the concept we propose is consistent by discretization in time with the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5661","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":"1404.5661","created_at":"2026-05-18T02:53:28.225522+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.5661v1","created_at":"2026-05-18T02:53:28.225522+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5661","created_at":"2026-05-18T02:53:28.225522+00:00"},{"alias_kind":"pith_short_12","alias_value":"3RNNNCAWNY56","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_16","alias_value":"3RNNNCAWNY56L44X","created_at":"2026-05-18T12:28:11.866339+00:00"},{"alias_kind":"pith_short_8","alias_value":"3RNNNCAW","created_at":"2026-05-18T12:28:11.866339+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/3RNNNCAWNY56L44X4U5YOZW24Q","json":"https://pith.science/pith/3RNNNCAWNY56L44X4U5YOZW24Q.json","graph_json":"https://pith.science/api/pith-number/3RNNNCAWNY56L44X4U5YOZW24Q/graph.json","events_json":"https://pith.science/api/pith-number/3RNNNCAWNY56L44X4U5YOZW24Q/events.json","paper":"https://pith.science/paper/3RNNNCAW"},"agent_actions":{"view_html":"https://pith.science/pith/3RNNNCAWNY56L44X4U5YOZW24Q","download_json":"https://pith.science/pith/3RNNNCAWNY56L44X4U5YOZW24Q.json","view_paper":"https://pith.science/paper/3RNNNCAW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.5661&json=true","fetch_graph":"https://pith.science/api/pith-number/3RNNNCAWNY56L44X4U5YOZW24Q/graph.json","fetch_events":"https://pith.science/api/pith-number/3RNNNCAWNY56L44X4U5YOZW24Q/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/3RNNNCAWNY56L44X4U5YOZW24Q/action/timestamp_anchor","attest_storage":"https://pith.science/pith/3RNNNCAWNY56L44X4U5YOZW24Q/action/storage_attestation","attest_author":"https://pith.science/pith/3RNNNCAWNY56L44X4U5YOZW24Q/action/author_attestation","sign_citation":"https://pith.science/pith/3RNNNCAWNY56L44X4U5YOZW24Q/action/citation_signature","submit_replication":"https://pith.science/pith/3RNNNCAWNY56L44X4U5YOZW24Q/action/replication_record"}},"created_at":"2026-05-18T02:53:28.225522+00:00","updated_at":"2026-05-18T02:53:28.225522+00:00"}