Uniqueness of the BRT Electromagnetic Inverse-Coupling Scalar from Idempotent Grassmannian Geometry

This record contains the paper “Uniqueness of the BRT Electromagnetic Inverse-Coupling Scalar from Idempotent Grassmannian Geometry.” Within the framework of Boundary Relativity Theory (BRT), the paper introduces an axiomatic definition of the BRT electromagnetic inverse-coupling scalar based on a rank-4 Hermitian idempotent P² = P on C^15. It proves that the BRT-internal dimensionless quantity satisfying five structural axioms is unique, with the exact rational value α⁻¹_BRT = 78,562,738,823 / 573,300,004 = 137.035999084. The leading structural term α⁻¹_struct = k² + (N−k)² = 137 is selected by structural classification, and the admissible feedback structure uniquely corrects it to the full value 137.035999084. The paper distinguishes between the internal uniqueness theorem for the BRT quantity and its conditional physical identification with the fine-structure constant, which depends on the low-energy U(1)_em sector of BRT being realized as QED. The result is presented as a parameter-free rational-number prediction, directly falsifiable digit by digit against future precision measurements. Keywords Boundary Relativity Theory、BRT、fine-structure constant、electromagnetic inverse-coupling scalar、idempotency、P2=P、Grassmannian geometry、 Hermitian idempotent、composite gauge field、structural classification、parameter-free prediction、QED correspondence、alpha inverse、α−1