Geometric Origin of the Universal Exponent α = sin(π/8) in Mem-force Theory

In Mem-force Theory (MFT) V1-V5, the universal exponent α is obtained from fitting the rotation curves of 15 SPARC galaxies, yielding α = 0.385 ± 0.02. This paper notes that this value coincides with the geometric constant sin(π/8) = 0.382683 to within 0.6%. Starting from the complete action of MFT, combined with renormalization group (RG) flow analysis and eightfold symmetric (D₈) geometry, we derive α = sin(π/8). This derivation elevates α from a phenomenological fitting parameter to a theoretically constrained constant rooted in geometry and group theory, rendering all predictions of MFT (glueball masses, dark energy equation of state, cosmic void expansion differences) parameter-free. All core assumptions are explicitly stated. Future high-precision data from SKA and Euclid will directly test the central prediction of the theory.