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In the proof, we establish Ozawa--Popa and Popa--Vaes's weakly compact action on the continuous core of $N \\otimes B$ as the one relative to B, by using an operator valued weight to B and the central weak am"},"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":"1607.02847","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-07-11T07:58:34Z","cross_cats_sorted":[],"title_canon_sha256":"8eb237d9aba8121be250756655d80c31eec571f9d47e1534e22f1d153cfacfbc","abstract_canon_sha256":"252be7ba66a9581d18bc5863e2e8f4f6bde0959173788c1e4e5c843f10bb2075"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:54:57.080790Z","signature_b64":"wNewv49UlYwJBWwAYk3sLt8vGZnUBVPyS2oywoU7I3b3JP8pHbPGN121FyK82FH8UzK9UWJZ2pq4b4YWZdstCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"23e0f751b2923ebdd72dddf61efcc8470b77fdbe3330a617f610b2a50b1cc3a8","last_reissued_at":"2026-05-17T23:54:57.080120Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:54:57.080120Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Cartan subalgebras of tensor products of free quantum group factors with arbitrary factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Yusuke Isono","submitted_at":"2016-07-11T07:58:34Z","abstract_excerpt":"Let $\\mathbb{G}$ be a free (unitary or orthogonal) quantum group. 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