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In the non-Brjuno case, we prove that a pseudo-rotation of class $C^k$, $k\\geq 2$, is $C^{k-1}$-rigid using the simple observation, derived from Franks' Lemma on free discs, that a pseudo-rotation with small rotation number compared to its $C^1$ (or H\\\"older) norm must be close to Identity.\n  From our result and a structure theorem"},"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":"1509.06906","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-09-23T10:04:54Z","cross_cats_sorted":[],"title_canon_sha256":"2f54f0bdb81ebbdd719965d53a2ebaa9e71e88bd638e7d384b3420ad3c7ebeed","abstract_canon_sha256":"9fd8360a2578a750d3dc0ce37633c49a2861050fb117cc1f4466f8e194896b2b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:32:17.557041Z","signature_b64":"KaJxIjBI/DI33lWxhhO4qz2w75gJFhQFc/jYTC1lycI3MM9c7fa8SFIQe8SN60vnyyNPJW3EDTytBCbdXxiMDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"82d9e15d6c1db0b1eecdea3675b91d3b9e88c71cc0b27348cd161ced48bef772","last_reissued_at":"2026-05-18T01:32:17.556298Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:32:17.556298Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On mixing diffeomorphisms of the disk","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"A. 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