Published January 7, 2026 | Version v1

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Description

Two independent derivations—N = α⁻¹/ln(2) from electromagnetism and N = 6 × 3 × 11 from spacetime geometry—converge on the same 198-bit information-geometric architecture (a finite bit-indexed geometric structure whose channel widths k determine mass scales via m/mₚ = exp(−198/k)). A leading-order estimate gives α⁻¹ ≈ N ln(2); applying the observation offset τ yields α⁻¹ = (197 + ln(2)) × ln(2) = 137.0304 (0.004% error). From this architecture, I derive 65+ fundamental quantities with zero free parameters: the electron mass via kₑ = 4 − (1/2π)(1 − α) = 3.842 (0.8% error); the Higgs mass via k_H = 5 + (1/16)(1 − α) = 5.062 (0.4% error); the strong coupling α_s = 0.1181 (0.2% error); the weak mixing angle sin²θ_W = 3/13 (0.2% error); the complete CKM matrix via Wolfenstein parameters λ = 9/40, A = 4/5, ρ = 1/7, η = 4/11 (all <2% error); the complete PMNS matrix via sin²θ₁₂ = 1/3, sin²θ₂₃ = 1/2 + η/8, sin θ₁₃ = 3/(k₁×k₃) (errors 0.2°–5.5°); the complete electroweak scale via constraint running and Yukawa saturation (m_W = 79.8 GeV, 0.7% error; m_Z = 91.0 GeV, 0.2% error); the Higgs potential parameters (λ_H = 0.131, 1.6% error); the dark energy scale ρ_Λ^(1/4) ≈ 1.9 meV (17% error); proton stability (τ_p ≫ 10³⁴ yr); all Z-pole asymmetry parameters; QCD running at multiple energy scales (1.6% average error); and gravitational coupling κ = 1/8π. The generation law k_n = 4 + (4/9)(n−1) unifies quark and lepton mixing. A key discovery: A = 4/5 governs both CKM mixing and QCD confinement. M-theory’s 11 dimensions emerge as d = 3 spatial + 8 SU(3) color.

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