A Complete Theory of CP Violation Derived from the Riemann Harmonic Sphere and the Harmonic Structure of Number Space

This paper presents a first-principles geometric theory that derives CP violation (the matter-antimatter asymmetry of elementary particles) from the structure of the adopted parent geometry G_ado, with zero free parameters.

The eight geometric constants {r=π/8, a/r=3/(2π²), Δθ_K=1/12, C_j=π²/128, α=√(π/2), K=2/3, λ_eff=(8/π)⁴-3/4, θ_{K,up}=rμ_k} reproduce all seven CKM observables within at most 0.45σ of the PDG measurements (χ²_7 = 0.461).

Key results:

• Berry holonomy formula Φ_B = -2π(s_f + λ_f β(θ)) cos θ derived through a six-step lemma chain from G_ado
• Three generations enforced geometrically via PSL(2,7) ⊂ SU(3)
• Electromagnetic correction coefficients 12/7, π/2, 3π/4 derived exactly from the heat-kernel coupling and Fano/Koide structure
• Maxwell's equations in null form (closure on the null time direction)

The paper consists of 12 main chapters and 20 supplementary chapters (approximately 270 pages). Both Japanese and English versions are provided.

This work is built on the framework of the preliminary research, the Riemann harmonic sphere reformulation (DOI: 10.5281/zenodo.19035966).

日本語要旨: 本論文は、CP 対称性の破れを採用親幾何 G_ado 上の幾何学的構造から、ゼロ自由パラメータで導出する理論を提示する。8 個の幾何定数のみから CKM 行列 7 観測量を χ²_7 = 0.461 (最大 0.45σ) で再現する。主章 12 + 補強章 20 (約 270 ページ)、日英両言語版を提供。