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Then for $a, b \\in A^+ \\setminus\\{ 0 \\}$, we have $a b = 0$ if and only is $\\Vert \\Vert c \\Vert^{-1} c + \\Vert d \\Vert^{-1} d \\Vert = 1$ whenever $0 < c \\le a$ and $0 < d \\le b$ in $A^+$."},"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":"1705.02046","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2017-05-04T23:30:44Z","cross_cats_sorted":[],"title_canon_sha256":"cb291b19c51ca97469daedaa1cd1c34a6d10974891f981f50ad0d3c70aefc794","abstract_canon_sha256":"aaa344fdedc8d2656b751708357188aa72b9d3fe03036984977ad1ab69ae7a39"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:27:52.577437Z","signature_b64":"q4QXGuiMScHJbek6BB8SoMVHNvJqsolsom9NF7OxZ0mRXQxr32Ql4PdHSK9f4299noMsr3Z3lcKIn6l9bbtPCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0b48b5bed05911d2d766683e357bbe5441af6d0879d65fa74c1e962a0fc3a268","last_reissued_at":"2026-05-18T00:27:52.576818Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:27:52.576818Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Algebraic orthogonality in $C^{\\ast}$--algebras-II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Anil Kumar Karn","submitted_at":"2017-05-04T23:30:44Z","abstract_excerpt":"We prove the following: Let $A$ be a C$^{\\ast}$-algebra. 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