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The theory for $(B,\\beta)$ is analogous to the theory of classic crossed products by automorphisms, and the key idea is to describe the counterparts of classic notions for $(B,\\beta)$ in terms of the initial system $(A,\\alpha)$.\n  We apply this idea to study the ideal structure of a non-unital version of the crossed 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":"1404.4928","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2014-04-19T06:53:25Z","cross_cats_sorted":[],"title_canon_sha256":"219af9528822aa9f5ff230e064d79addad24e870bd11e50c52e44ec2e43bbb06","abstract_canon_sha256":"08b08d1a2d64a1190c048fdc47a36f0493f67b47ed189a16ef56ae4988c0e404"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:17:43.150196Z","signature_b64":"9411TGpe6/EgA1LEDbdvag9UUJ4f0kB3J2H0GV16MMsvS06FwRQwJ/p4BBQ4wxG6z6II0FWLGnPkIVOLpnw5AQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"226c6e61a8f427e800f389244a462e90ca494c4af748deba1d5190fdd25ffc20","last_reissued_at":"2026-05-18T02:17:43.149735Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:17:43.149735Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Ideal structure of crossed products by endomorphisms via reversible extensions of $C^*$-dynamical systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"B. 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