Structural Obstructions in the Substrate Instanton Route to the Fine-Structure Constant

A semiclassical instanton construction within the substrate geometric framework yields the exact conditional value α −¹cond = e^π²/2^π³/2/4√2 = 136.870 . . . provided one assumes the reduced scale A = π⁴/256. We prove here that this scale cannot be derived from the compact scalar parent phase action by dimensional reduction over any transverse fiber geometry. We further show that weak Randers anisotropy consistent with the weak equivalence principle cannot generate the required order-one correction, and that Abelian Hopf/Chern–Simons topological terms reduce only to boundary or Berry-phase contributions, leaving the stiffness-to mass ratio unchanged. These results establish a no-go theorem: all natural geometric completion mechanisms within the present substrate instanton architecture are excluded.