Determination of the Geometric Coefficient from Twisted Fibrations in 15D Rotational‑Order Geometry

Building upon Paper 44’s Kaluza‑Klein reduction for the 15‑dimensional metric‑affine action, this work investigates the topological origin of the geometric coefficient c₁. The coefficient originates from the twisting of the internal S³ fibre over the six‑dimensional flag manifold F₁,₂. Evaluating characteristic classes on the internal base manifold demonstrates that c₁ is a pure topological invariant related to the Euler characteristic of F₁,₂, removing c₁ as a free parameter of the theory. Remaining dependencies of the effective coupling η upon compactification moduli (internal‑space volumes, 15‑dimensional Planck mass) are dynamical moduli fixed by cosmological evolution rather than Lagrangian free parameters. This paper completes the core mathematical foundation for the rotational‑order geometric framework.