Geometric Reconstruction of CKM Mixing and CP Violation from a Discrete H4/Fibonacci Framework with an Exploratory Extension to PMNS Mixing

Abstract This paper presents a discrete-geometric reconstruction of the flavor-mixing sector within the UNIVERSE131 framework. It proposes that the hierarchical structure of the CKM matrix and the origin of the three generations are not arbitrary parameters, but emerge from the ratio structure of low Fibonacci numbers and the fivefold symmetry of the H4/600-cell polytope. Core Findings (Layer A/B) The model assigns exact geometric values to fundamental mixing parameters, achieving benchmark agreement within a few percent for the leading-order CKM data: Cabibbo Parameter (): Assigned the exact rational value F₄/F₇ = 3/13 0. 2308. CP Phase (₂₏): Assigned the geometric angle (^-2) 67. 54^. Unitarity Triangle Radius (|+i|): Set to ^-2 0. 3820, consistent with experimental fits. Generation Count: The existence of exactly three generations is associated with the factorization of the Pisano period (9) = 24 = 3 8. Exploratory Extensions (Layer C) The paper records an extension to the leptonic (PMNS) sector. While the solar mixing angle is reproduced with high accuracy (33. 7^), the reactor and atmospheric sectors are treated as exploratory directions for future work. Methodology and Reproducibility Following the calibrated claim hierarchy of the program, the paper maintains a strict boundary between robust algebraic statements and phenomenological readings. To ensure reproducibility while protecting the proprietary source implementation, the paper provides explicit mathematical definitions and a complete algorithmic protocol for independentverification.