{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2005:TLDQRT5SEQR7U5GDWIUBI4L7KE","short_pith_number":"pith:TLDQRT5S","schema_version":"1.0","canonical_sha256":"9ac708cfb22423fa74c3b22814717f5114edcc93a08656f4cd71af42bdedcc0e","source":{"kind":"arxiv","id":"math/0506063","version":3},"attestation_state":"computed","paper":{"title":"Sur la dynamique unidimensionnelle en r\\'egularit\\'e interm\\'ediaire","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Andres Navas, Bertrand Deroin, Victor Kleptsyn","submitted_at":"2005-06-03T13:06:31Z","abstract_excerpt":"Using probabilistic methods, we prove new rigidity results for groups and pseudo-groups of diffeomorphisms of one dimensional manifolds with intermediate regularity class ({\\em i.e.} between $C^1$ and $C^2$). In particular, we demonstrate some generalizations of Denjoy's Theorem and the classical Kopell's Lemma for Abelian groups. After that, these techniques are applied to the study of codimension 1 foliations. We obtain for instance several generalized versions of Sacksteder's Theorem in class $C^1$. We conclude with some remarks about the stationary measure."},"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":"math/0506063","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"2005-06-03T13:06:31Z","cross_cats_sorted":[],"title_canon_sha256":"ecf9557019ed507151cd9e557d93a7080557cbb5a5937f8827f42640e6e0770c","abstract_canon_sha256":"fbd4d6ccfc45b33a09d54c33b5c77554c138173516848a2b002c61406eb1611d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:05:28.349494Z","signature_b64":"AP0KIqWEf54x7+CNLLFdpkv1xBmsdWgQWRJElTvw0ehlJLUvhvP+DJs3ODR1Z0gfZLGeddIYD7vWeiTHgtogDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9ac708cfb22423fa74c3b22814717f5114edcc93a08656f4cd71af42bdedcc0e","last_reissued_at":"2026-05-18T04:05:28.348757Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:05:28.348757Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sur la dynamique unidimensionnelle en r\\'egularit\\'e interm\\'ediaire","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Andres Navas, Bertrand Deroin, Victor Kleptsyn","submitted_at":"2005-06-03T13:06:31Z","abstract_excerpt":"Using probabilistic methods, we prove new rigidity results for groups and pseudo-groups of diffeomorphisms of one dimensional manifolds with intermediate regularity class ({\\em i.e.} between $C^1$ and $C^2$). In particular, we demonstrate some generalizations of Denjoy's Theorem and the classical Kopell's Lemma for Abelian groups. After that, these techniques are applied to the study of codimension 1 foliations. We obtain for instance several generalized versions of Sacksteder's Theorem in class $C^1$. We conclude with some remarks about the stationary measure."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0506063","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":"math/0506063","created_at":"2026-05-18T04:05:28.348872+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/0506063v3","created_at":"2026-05-18T04:05:28.348872+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0506063","created_at":"2026-05-18T04:05:28.348872+00:00"},{"alias_kind":"pith_short_12","alias_value":"TLDQRT5SEQR7","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_16","alias_value":"TLDQRT5SEQR7U5GD","created_at":"2026-05-18T12:25:53.335082+00:00"},{"alias_kind":"pith_short_8","alias_value":"TLDQRT5S","created_at":"2026-05-18T12:25:53.335082+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/TLDQRT5SEQR7U5GDWIUBI4L7KE","json":"https://pith.science/pith/TLDQRT5SEQR7U5GDWIUBI4L7KE.json","graph_json":"https://pith.science/api/pith-number/TLDQRT5SEQR7U5GDWIUBI4L7KE/graph.json","events_json":"https://pith.science/api/pith-number/TLDQRT5SEQR7U5GDWIUBI4L7KE/events.json","paper":"https://pith.science/paper/TLDQRT5S"},"agent_actions":{"view_html":"https://pith.science/pith/TLDQRT5SEQR7U5GDWIUBI4L7KE","download_json":"https://pith.science/pith/TLDQRT5SEQR7U5GDWIUBI4L7KE.json","view_paper":"https://pith.science/paper/TLDQRT5S","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/0506063&json=true","fetch_graph":"https://pith.science/api/pith-number/TLDQRT5SEQR7U5GDWIUBI4L7KE/graph.json","fetch_events":"https://pith.science/api/pith-number/TLDQRT5SEQR7U5GDWIUBI4L7KE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TLDQRT5SEQR7U5GDWIUBI4L7KE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TLDQRT5SEQR7U5GDWIUBI4L7KE/action/storage_attestation","attest_author":"https://pith.science/pith/TLDQRT5SEQR7U5GDWIUBI4L7KE/action/author_attestation","sign_citation":"https://pith.science/pith/TLDQRT5SEQR7U5GDWIUBI4L7KE/action/citation_signature","submit_replication":"https://pith.science/pith/TLDQRT5SEQR7U5GDWIUBI4L7KE/action/replication_record"}},"created_at":"2026-05-18T04:05:28.348872+00:00","updated_at":"2026-05-18T04:05:28.348872+00:00"}