Explicit Kaluza‑Klein Reduction of the 15‑Dimensional Metric‑Affine Action in Rotational‑Order Geometry

We perform the rigorous Kaluza‑Klein (KK) reduction of the 15‑dimensional metric‑affine action down to four dimensions within the rotational‑order geometric unification framework. By explicitly decomposing the 15D metric on the product manifold, including the dependence of the internal metric on the orientation field n^a(x), we compute the 15D Ricci scalar and integrate over the 11 internal dimensions. We show that the effective coupling η and the correlation length r_c emerge as pure geometric quantities determined by the internal volume V_11 and the S³ fiber volume V_S³. This establishes a first‑principles geometric framework for the effective parameters. The remaining coefficient c_1 is derived from the twisted fibration geometry, with its exact numerical value to be determined in future work. This paper solidifies the mathematical foundation of the framework.