Parameter-Free Derivation of CKM Mixing Angles from Cayley-Dickson Topology and Möbius Fiber Spectrum

Abstract

This paper constructs a canonical isomorphism between the Laplace spectrum on a Möbius fiber and the Cayley-Dickson nilpotent decomposition, proving that CKM matrix elements are topological invariants—specifically cross-ratios on the Fano plane—under this isomorphism. As a corollary, the Cabibbo angle is determined parameter-free as ∣V us ∣=3/√ 170≈0.2301. This result follows from a single ontological postulate—that every spacetime point is a Möbius Point-Embryo B=(0,1)—without recourse to any experimentally fitted parameters. Unlike purely algebraic models such as Furey (2018), the corrections in this work originate from the eigen-spectrum of the Möbius fiber, not from ad hoc normalization choices in the algebra.