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Motivated by orthogonal versions of the James constant, we introduce the weighted Birkhoff orthogonal James-type constant $$J_\\lambda^{\\perp}(X)=\\sup \\left\\{\\min \\{\\|\\lambda x+(1-\\lambda) y\\|,\\|\\lambda x-(1-\\lambda) y\\|\\}: x, y \\in S_X, x \\perp_B y\\right\\},$$ where \\(\\lambda\\in[0,1]\\) and $x \\perp_B y$ stands for Birkhoff orthogonality. We establish its basic bounds, stability properties, and reduction principles, and clarify its relations with the orthogonal James constant $J_{\\perp}(X)$. The 2 -Lipschitz continuity of $J_\\lambda^{\\perp}("},"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":"2606.01068","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2026-05-31T07:22:57Z","cross_cats_sorted":[],"title_canon_sha256":"e94f3b90b4322b42c58316e4f878d1a075be6d00751b92d1812121d984d17eab","abstract_canon_sha256":"791eb7c1a703a82048dbf2b292a7c72db654894c85e843d1f631864efd963071"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-02T01:04:20.405153Z","signature_b64":"AhSQqsA2NqgTL/XhYMgFbEl+Tqba/+b+5MHsdnZJ2ujlq80/joJ5nFl/7Fyd5BIvPvKym9wozTMNX3F6PICiDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c3bbbd3f3dc1c99b91fed4c043257b3027cb111211df4a75d18ae51a50a2958e","last_reissued_at":"2026-06-02T01:04:20.404740Z","signature_status":"signed_v1","first_computed_at":"2026-06-02T01:04:20.404740Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A weighted Birkhoff orthogonal James-type constant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Junxiang Qi, Qi Liu, Yongjin Li, Zhouping Yin","submitted_at":"2026-05-31T07:22:57Z","abstract_excerpt":"Let $X$ be a real Banach space and $\\lambda \\in[0,1]$. Motivated by orthogonal versions of the James constant, we introduce the weighted Birkhoff orthogonal James-type constant $$J_\\lambda^{\\perp}(X)=\\sup \\left\\{\\min \\{\\|\\lambda x+(1-\\lambda) y\\|,\\|\\lambda x-(1-\\lambda) y\\|\\}: x, y \\in S_X, x \\perp_B y\\right\\},$$ where \\(\\lambda\\in[0,1]\\) and $x \\perp_B y$ stands for Birkhoff orthogonality. We establish its basic bounds, stability properties, and reduction principles, and clarify its relations with the orthogonal James constant $J_{\\perp}(X)$. 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