{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:UCVWXHHX7MBK3ZPHAY7JZTXDKT","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":"8cf0ea9a6577fae1ca43e29d7bbd38555a21b229e5786d045b4751c3fe36a852","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-30T17:18:17Z","title_canon_sha256":"c6a8f6ad2dfbc251bb4f5cfaef6ab47bb3f3fb184d86c62d406d367dbc46a637"},"schema_version":"1.0","source":{"id":"1307.8055","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.8055","created_at":"2026-05-18T03:17:12Z"},{"alias_kind":"arxiv_version","alias_value":"1307.8055v1","created_at":"2026-05-18T03:17:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.8055","created_at":"2026-05-18T03:17:12Z"},{"alias_kind":"pith_short_12","alias_value":"UCVWXHHX7MBK","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"UCVWXHHX7MBK3ZPH","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"UCVWXHHX","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:05e7ef84e50de012fe22f9e3a67f94a4424273ecbf9d19eed5607b4161e4a390","target":"graph","created_at":"2026-05-18T03:17:12Z","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 consider special flows over the rotation on the circle by an irrational $\\alpha$ under roof functions of bounded variation. The roof functions, in the Lebesgue decomposition, are assumed to have a continuous singular part coming from a quasi-similar Cantor set (including the Devil's staircase case). Moreover, a finite number of discontinuities is allowed. Assuming that $\\alpha$ has bounded partial quotients, we prove that all such flows are weakly mixing and enjoy weak Ratner's property. Moreover, we provide a sufficient condition for the roof function to obtain a stability of the cocycle R","authors_text":"Adam Kanigowski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-30T17:18:17Z","title":"Ratner's property for special flows over irrational rotations under functions of bounded variation. II"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.8055","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:fb7002ebd03ab8eaeaea2bdffe8031bb05f89bda11c8f3280fe05331af114c6a","target":"record","created_at":"2026-05-18T03:17:12Z","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":"8cf0ea9a6577fae1ca43e29d7bbd38555a21b229e5786d045b4751c3fe36a852","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-07-30T17:18:17Z","title_canon_sha256":"c6a8f6ad2dfbc251bb4f5cfaef6ab47bb3f3fb184d86c62d406d367dbc46a637"},"schema_version":"1.0","source":{"id":"1307.8055","kind":"arxiv","version":1}},"canonical_sha256":"a0ab6b9cf7fb02ade5e7063e9ccee354cef089f078073a9f8214cb54f0989d4c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"a0ab6b9cf7fb02ade5e7063e9ccee354cef089f078073a9f8214cb54f0989d4c","first_computed_at":"2026-05-18T03:17:12.519573Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:17:12.519573Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"3EM74xcmF7xHU7iK4H2VpccarJDj9qlz7WyDQOOtGZhqzPR8JhU1Wb35/Wm9uAo/TbC7wbdssGAwkiT/6JvgDA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:17:12.520288Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.8055","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:fb7002ebd03ab8eaeaea2bdffe8031bb05f89bda11c8f3280fe05331af114c6a","sha256:05e7ef84e50de012fe22f9e3a67f94a4424273ecbf9d19eed5607b4161e4a390"],"state_sha256":"4ba979daf5c1b7b5319a9efdcbdc00b2b1dcfe42bc950631018ec2a1163e8089"}