{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:APFKFC44AEVS2MINQU3GJU6ALX","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":"1b39665b80c106247f2588ac4f2ab028f978df14cfc421eea5b39c3c2a765ee5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-01T15:30:15Z","title_canon_sha256":"5c25832081f85d5a0ea7c91f09d86e2a2ce3c6fbaa67bebe9b3ab8c294d46c6b"},"schema_version":"1.0","source":{"id":"1306.0123","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.0123","created_at":"2026-05-18T03:21:56Z"},{"alias_kind":"arxiv_version","alias_value":"1306.0123v1","created_at":"2026-05-18T03:21:56Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.0123","created_at":"2026-05-18T03:21:56Z"},{"alias_kind":"pith_short_12","alias_value":"APFKFC44AEVS","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_16","alias_value":"APFKFC44AEVS2MIN","created_at":"2026-05-18T12:27:38Z"},{"alias_kind":"pith_short_8","alias_value":"APFKFC44","created_at":"2026-05-18T12:27:38Z"}],"graph_snapshots":[{"event_id":"sha256:780bed575cb59ccad4e3f2af51813f9c36277a84f570ebbf986409961f79adc4","target":"graph","created_at":"2026-05-18T03:21:56Z","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":"Let $(M, \\mathcal{F})$ be a compact Riemannian foliated manifold. We consider a family of compatible Feller semigroups in $C(M^n)$ associated to laws of the $n$-point motion. Under some assumptions (Le Jan and Raimond, \\cite{Le Jan-Raimond}) there exists a stochastic flow of measurable mappings in $M$. We study the degeneracy of these semigroups such that the flow of mappings is foliated, i.e. each trajectory lays in a single leaf of the foliation a.s, hence creating a geometrical obstruction for coalescence of trajectories in different leaves. As an application, an averaging principle is prov","authors_text":"Paulo Henrique P da Costa, Paulo R. Ruffino","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-01T15:30:15Z","title":"Degenerate semigroups and stochastic flows of mappings in foliated manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0123","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":"sha256:26cf7552362c682d8a43c29590a0656244a106da337c4064127c1bd6c0064b1f","target":"record","created_at":"2026-05-18T03:21:56Z","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":"1b39665b80c106247f2588ac4f2ab028f978df14cfc421eea5b39c3c2a765ee5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-06-01T15:30:15Z","title_canon_sha256":"5c25832081f85d5a0ea7c91f09d86e2a2ce3c6fbaa67bebe9b3ab8c294d46c6b"},"schema_version":"1.0","source":{"id":"1306.0123","kind":"arxiv","version":1}},"canonical_sha256":"03caa28b9c012b2d310d853664d3c05dd867338e0c73baf4433f92c8abf01077","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"03caa28b9c012b2d310d853664d3c05dd867338e0c73baf4433f92c8abf01077","first_computed_at":"2026-05-18T03:21:56.076231Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:56.076231Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tAKnf+nttD1PuLyhg3xWBJ5CTHus1vQywNbMSnLcYkXY3yaDaUExMLdAQP4jXA0nIv+o47H930xkzYKiIFwqCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:56.076775Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.0123","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:26cf7552362c682d8a43c29590a0656244a106da337c4064127c1bd6c0064b1f","sha256:780bed575cb59ccad4e3f2af51813f9c36277a84f570ebbf986409961f79adc4"],"state_sha256":"819056eab5aacc31150aa23dddcd039040e1a2330312209844791891df8a03c4"}