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Suppose $\\af$ and $\\bt$ are two automorphisms with the Rokhlin property that {induce the same action on the $K$-theoretical data of $A$.} We show that $\\af$ and $\\bt$ are strongly cocycle conjugate and uniformly approximately conjugate, that is, there exists a sequence of unitaries $\\{u_n\\}\\subset A$ and a sequence of strongly asymptotically inner automorphisms $\\sigma_n$ such that $$ \\af={\\rm Ad}\\, u_n\\circ \\sigma_n\\circ \\bt\\circ \\sigma_n^{-1}\\andeqn \\l"},"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":"1305.4994","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-05-22T00:42:56Z","cross_cats_sorted":[],"title_canon_sha256":"931013e697e33a91f630123767152eb322631b23214d5d5fdf917593cee85657","abstract_canon_sha256":"47b8a1ea7dbac9df5341202f4906f4750804acb5ce2d6327ff71a11905df4248"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:44.628915Z","signature_b64":"OXJqdLa+RvTwH2dBbBphGi88tu3X5FoCsBl6No57gh6XV71IAI69L5OWRFkLdGEY8p8lIitHDW0hJwrzK7xkBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fdd004cdf33efc26c629399a0a1ebfec356373e216d263c677f3fb9a5720ed72","last_reissued_at":"2026-05-18T03:06:44.627729Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:44.627729Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Kishimoto's Conjugacy Theorems in simple $C^*$-algebras of tracial rank one","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Huaxin Lin","submitted_at":"2013-05-22T00:42:56Z","abstract_excerpt":"Let $A$ be a unital separable simple amenable $C^*$-algebra with finite tracial rank which satisfies the Universal Coefficient Theorem (UCT). 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