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We prove that Kirchberg's formulation of Connes' embedding problem has a positive answer if and only if $\\mathcal{U}_{nc}(2) \\otimes_{\\min} \\mathcal{U}_{nc}(2)=\\mathcal{U}_{nc}(2) \\otimes_{\\max} \\mathcal{U}_{nc}(2)$. Our results follow from properties of the finite-dimensional operator system $\\mathcal{V}_n$ spanned by $1$ and the generators of $\\mathcal{U}_{nc}(n)$. We show that $\\mathcal{V}_n$ is an operator system quotient of $M_{2n}$ and has"},"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":"1608.03229","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2016-08-10T16:18:09Z","cross_cats_sorted":[],"title_canon_sha256":"0595312edff70a2d2df4f67b0ec8d55d8f75659514be36c769a1404560388d61","abstract_canon_sha256":"6da37ed93add2714159339f155c9dd2ba23b2b8acf4b063ce2d332071dfe5dad"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:26:18.513289Z","signature_b64":"QErahq8dmeNWztZP+4RR3/B93RU/9jOLXUirFgb1f4mB9DzrM58zEvVNFUN8MxaBRgM0w5GFhzQvzFxzzOuIAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e8154066640663dbcf9dd36919bb9016f09f5e2a8ace916dad3260e1d01ba43a","last_reissued_at":"2026-05-18T00:26:18.512802Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:26:18.512802Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Non-Commutative Unitary Analogue of Kirchberg's Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Samuel J. 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