A Structural Derivation of the Fine-Structure Constant as a Geometric Invariant of the BRISM Interface

* * * This Verison v1.2 is superseded by v1.21ff * * * This work presents a structural derivation of the electromagnetic fine‑structure constant within the BRISM framework (BRane Interface Substrate Model). BRISM interprets the observable world as a phase‑neutral, positive and σ‑additive projection of unitary bulk states (Naimark–Stinespring dilation), under which the Born probability law emerges as the unique stable interface measure. Applying the same interface axioms to the coupling structure yields a closed, parameter‑free identity for the inverse fine‑structure constant. Three geometric contributions — the bulk‑volume term, the brane‑metric term, and the U(1) phase‑residuum — together with a phase‑neutral normalization across the two bulk half‑spaces, determine the parameter‑free identity: Numerical evaluation gives: α⁻¹ = 137.036 DOI 10.5281/zenodo.18730271