{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3RNNNCAWNY56L44X4U5YOZW24Q","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":"54f6e2867ca74c331802ba0fe190339643a730bb0f7cd19c48d30295540c85a7","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-04-22T21:59:25Z","title_canon_sha256":"8080716cb87c1201a53c44b34e7a8938ea29a0e37d80e6fcf523b518abb08913"},"schema_version":"1.0","source":{"id":"1404.5661","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.5661","created_at":"2026-05-18T02:53:28Z"},{"alias_kind":"arxiv_version","alias_value":"1404.5661v1","created_at":"2026-05-18T02:53:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.5661","created_at":"2026-05-18T02:53:28Z"},{"alias_kind":"pith_short_12","alias_value":"3RNNNCAWNY56","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3RNNNCAWNY56L44X","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3RNNNCAW","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:1f3139fca81e493371d9fa06eacf2237aaff2ef9dbe07db4c259e03ed5975baa","target":"graph","created_at":"2026-05-18T02:53:28Z","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":"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 ","authors_text":"Paulo R. C. Ruffino","cross_cats":["math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-04-22T21:59:25Z","title":"A Sampling Theorem for Rotation Numbers of Linear Processes in ${\\R}^{2}$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.5661","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:cb0af96dc4fabd8187dea6af977f7ac1188586de477522d07dd4fc6d7ec2bb1a","target":"record","created_at":"2026-05-18T02:53:28Z","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":"54f6e2867ca74c331802ba0fe190339643a730bb0f7cd19c48d30295540c85a7","cross_cats_sorted":["math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2014-04-22T21:59:25Z","title_canon_sha256":"8080716cb87c1201a53c44b34e7a8938ea29a0e37d80e6fcf523b518abb08913"},"schema_version":"1.0","source":{"id":"1404.5661","kind":"arxiv","version":1}},"canonical_sha256":"dc5ad688166e3be5f397e53b8766dae400722678115cf395cedf80dc24659277","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"dc5ad688166e3be5f397e53b8766dae400722678115cf395cedf80dc24659277","first_computed_at":"2026-05-18T02:53:28.225399Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:53:28.225399Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"bjsGPDcgNPCgZLZr+kN67lDnUR66/c2pBNCH7ibo9/WAMKKuRz8w4qAGhCIJT1Hvx9IP6M5BIwjjHowN2YBUAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:53:28.226050Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.5661","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cb0af96dc4fabd8187dea6af977f7ac1188586de477522d07dd4fc6d7ec2bb1a","sha256:1f3139fca81e493371d9fa06eacf2237aaff2ef9dbe07db4c259e03ed5975baa"],"state_sha256":"4bd5ed4407a24d5b889cd3349c1bb95758d8849e2a5657a2b646719177618f40"}