The Higher‑Dimensional Origin of Effective Parameters in Rotational‑Order Geometry: A Framework

This paper addresses the origin of the two key effective parameters η and r_c used within rotational‑order geometric unification (Papers 39, 40). A 15‑dimensional metric‑affine manifold M₄×K¹¹ is adopted; after Kaluza‑Klein dimensional reduction, the dimensionless coupling η is linked to the ratio between internal‑field coupling and the 4‑dimensional Planck mass. The correlation length r_c corresponds to the inverse mass of the lowest‑lying Kaluza‑Klein excitation of the internal S³ fibre. This replaces purely phenomenological parameters with higher‑dimensional geometric quantities. Full dynamical derivation of the effective metric is postponed to future work. Consistency checks against prior astrophysical benchmark values are performed.