Calibrated Extension of the H4/GZ60 Discrete Algebraic Framework

This work presents Version 2 of Paper 017, a calibrated extension of the H4/GZ60 discrete algebraic framework. The framework investigates whether a 60-state cyclic algebraic system (12 × 5) can organize structures appearing in particle physics, atomic spectra, and discrete symmetry systems. The manuscript preserves and strengthens previously established theorem-level results of the program, including: A discrete SO (4) Casimir derivation reproducing the hydrogen spectrum. Exact generator-level algebra audits for SU (3) and SU (2) × U (1). A revised state dictionary providing an exact cover of the 48 fermionic degrees of freedom of the Standard Model. This exact cover uniquely determines Ngen = 3 and NH = 1, thereby reproducing the standard one-loop beta coefficients (b1, b2, b3) of the Standard Model gauge running. Paper 017 (Version 2) introduces crucial refinements in the flavor sector and CP violation: The gluon sector is explicitly organized as color-pair transitions consistent with the adjoint representation. The flavor sector is reformulated through a discrete overlap reconstruction rather than direct Yukawa diagonalization, yielding a stable reconstruction of all nine CKM magnitudes within 6% and the correct order of the Jarlskog invariant. A convention-calibrated CKM geometry is established, where the robust radius |ρ + iη| exactly matches the golden-ratio relation 1/φ² at the 10⁻³ level. NEW in v2 The CP violating phase is shown to admit a Next-to-Leading Order (NLO) algebraic expression: δCP ≈ arccos (1/φ² - λ²/2). This correction resolves the previous geometric residual, yielding a phase of 69. 17°, which matches the current experimental central value within 0. 03°. The purpose of this work is not to claim a completed unified dynamical theory, but to define a rigorous "claim boundary" for the H4/GZ60 program: explicitly separating which components are mathematically exact, which are supported by finite algebraic audits (Level A/B), and which remain open dynamical problems (such as the first-principles RGE origin of φ, and the mechanisms generating Majorana and Higgs masses).