2026/03/26 by Daniel Toupin · 1 voice
Mathematics · Social Sciences · Physics and Astronomy · #Algebraic and Geometric Analysis #International Science and Diplomacy #Quantum and Classical Electrodynamics
paper · doi:10.5281/zenodo.19246823
openalex publication_date 2026/03/26 · openalex created_date 2026/03/28 · openalex updated_date 2026/03/28
We demonstrate that the fundamental physical constants of the Standard Model are arithmetic invariants, originating from four mechanisms: (A) ratios of special values of L-functions in the Selberg class, (B) Bernoulli numbers transported by the archimedean Γ-factor via the functional equation, (C) ratios of nontrivial L-function zeros, and (D) dimensions of spaces of multiple zeta values counted by Zagier's recurrence. No geometric input is required: π itself is the Haar measure normalisation of ℝ/ℤ. At the GUT scale, the down-type quark mass ratios md : ms : mb = 2 : 5 : 9 follow exactly from the Casimir invariants C₂(n,0) = n(n+3)/3 of SU(3)flavor Kac–Moody representations for generations n = 1,2,3, and the Georgi–Jarlskog relation md mb/ms² = 9/4 matches experiment at 0.09%. The Cabibbo angle satisfies sin θ₁₂ = 1/(2√5) within 0.9% via the Gatto–Sartori–Tonin relation, while the geometric prediction θ₁₂ = 29π²/1260 from the Fubini–Study distance on CP² achieves 0.19%. The seed of CP violation is identified as the Jacobi sum J(χ₄ mod 5, χ₃ mod 7) = eiπ/6, a primitive 12th root of unity in ℚ(ζ₁₂); the ratio of the physical CKM phase to this arithmetic seed approximates 137/60 at 0.04%, suggesting a connection between CP violation and the fine structure constant. Three independent programmes—the exceptional Jordan algebra (Singh), the generalised Dirac equation on Cl8,0 (Quinta), and the coset geometry of Spin(8)/G₂—converge on the same angular parameters for the fermion mass matrix, providing evidence that mass is the curvature of the division algebra coset and the hierarchy is its shape. All numerical claims are verified at ≥ 15-digit precision.