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Using Takai duality we establish a stable isomorphism \\[ \\mathcal A\\rtimes_{\\alpha} \\Sigma \\sim_{s} \\big(\\mathcal A \\otimes \\mathcal K(\\mathcal G, \\Sigma, \\mu)\\big)\\rtimes_{\\alpha\\otimes {\\rm Ad}\\: \\rho} \\mathcal G, \\] where $\\mathcal K(\\mathcal G, \\Sigma, \\mu)$ denotes the compact operators in the CSL algebra ${\\rm Alg}\\:\\mathcal L(\\mathcal G, \\Sigma, \\mu)$ and $\\rho$ den"},"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":"1705.08729","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-05-24T12:44:02Z","cross_cats_sorted":[],"title_canon_sha256":"aa95ae9bd4a36376e9926e0719bc4a021ba3458c1a8599df1218e6b0d62217ce","abstract_canon_sha256":"853322117a07bf17edf06c63ac9d9aca7403dd48126892cef866a867eb0fd63d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:30.880045Z","signature_b64":"Md8sXppF+Jcy/DNRb1u390/j7nx5f8OGMZ+bHS7/5FqxU7RgFxXaE/VP2OPVYDGPbforySIa1KZgaVQ3HYx0Ag==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c6d6fae541d46806cfa93869f48eb720454c8796c3730c8f786a4714b0b8e560","last_reissued_at":"2026-05-18T00:32:30.879335Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:30.879335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Crossed products of operator algebras: applications of Takai duality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Christopher Ramsey, Elias Katsoulis","submitted_at":"2017-05-24T12:44:02Z","abstract_excerpt":"Let $(\\mathcal G, \\Sigma)$ be an ordered abelian group with Haar measure $\\mu$, let $(\\mathcal A, \\mathcal G, \\alpha)$ be a dynamical system and let $\\mathcal A\\rtimes_{\\alpha} \\Sigma $ be the associated semicrossed product. 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