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We show that for a \"generic\" $\\epsilon$H1, there exists an orbit ($\\theta$, p)(t) satisfying p(t) -- p(0) {\\textgreater} l(H1) {\\textgreater} 0, where l(H1) is independent of $\\epsilon$. The diffusion orbit travels along a co-dimension one resonance , and the only obstruction to our construction is a finite set of additional resonances. For the pr"},"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":"1701.05445","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-01-19T14:49:53Z","cross_cats_sorted":[],"title_canon_sha256":"f89d255fea0a0de06365eb3bae96b77c1dee0682d4a7708e9607cbfac8a68d38","abstract_canon_sha256":"1d5cedb6937f7337e2b06c1f0505bfdaba806e8784f4dd12ecf32afc2de02408"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:12.686853Z","signature_b64":"+f1OnaJe6rPlcYReliaoDjlOshBuNgj7/ifpdf4zsPQBlYWkDRJro4MqRQ9oVfaqvui361GpNEvG7tziEvIoCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9b62e196a7ac424596702a04ef211e3d4d78d4cc9b8fc194239515f3a2566755","last_reissued_at":"2026-05-18T00:52:12.686410Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:12.686410Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Arnold diffusion in arbitrary degrees of freedom and normally hyperbolic invariant cylinders","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"K Kaloshin, K Zhang, Patrick Bernard (DMA)","submitted_at":"2017-01-19T14:49:53Z","abstract_excerpt":"We prove a form of Arnold diffusion in the a priori stable case. Let H0(p) + $\\epsilon$H1($\\theta$, p, t), $\\theta$ $\\in$ T n , p $\\in$ B n , t $\\in$ T = R/T be a nearly integrable system of arbitrary degrees of freedom n 2 with a strictly convex H0. We show that for a \"generic\" $\\epsilon$H1, there exists an orbit ($\\theta$, p)(t) satisfying p(t) -- p(0) {\\textgreater} l(H1) {\\textgreater} 0, where l(H1) is independent of $\\epsilon$. The diffusion orbit travels along a co-dimension one resonance , and the only obstruction to our construction is a finite set of additional resonances. 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