This paper develops the physical consequences of the U(1) fiber in the five-dimensional quotient manifold M = (Im(H) × Sp(1))/U(1), whose spectral action reproduces 53 Standard Model quantities from one input (v = 246.22 GeV) and zero continuous free parameters Biswas, 2026, doi:10.5281/zenodo.19450091. Six results follow: (i) compactification of the quaternion configuration space to S³; (ii) CMB homogeneity from Hopf uniqueness; (iii) Lorentzian signature from u² = −1; (iv) the arrow of time — determined algebraically by the semigroup structure of the fiber (Proposition 1); (v) N = 60.2 inflationary e-foldings from the spectral hierarchy; and (vi) the total universe approximately 10⁹ times the observable radius. The Higgs quartic self-coupling is predicted at −0.55% with zero free parameters, and the Koide mass scale is derived at +0.33%.
Amit K. Biswas (Sun,) studied this question.