Systematic relations express Standard Model parameters through the golden ratio, highlighting experimental confirmations.
We present a systematic set of closed-form relations expressing 28 parameters of the Standard Model through the golden ratio φ = (1+√5)/2. The framework is based on a Fibonacci-structured scalar potential V_Art(s) = v⁴(s−1/φ²)²/(1−s−s²) and the Clifford algebra Cl(9,1) = Cl(3,1)⊗Cl(6), with the E₈(−24) → SU(9)/ℤ₃ decomposition independently confirmed by Wilson (2024). Nine results are derived from first principles with zero free parameters: the strong coupling αₛ = 1/(2φ³), the Weinberg angle sin²θ_W = 3/(8φ), the electroweak VEV v_EW = M_Pl/φ719/9, the hierarchy exponent 719/9 = 4×C(6,3)−1/9, the number of generations N_gen = 3 from the theorem N×2^N = (N+1)!, the Koide ratio Q = 2/3, the fine-structure constant tree level α⁻¹ = 360/φ², the weak coupling α₂⁻¹ = 135/φ³, and the integer constraint α₂⁻¹×α₃⁻¹ = 270. The vacuum position s₀ = 1/φ² is derived as the complement of the Fibonacci pole: s₀ = 1−s_pole. Three predictions have received experimental support: JUNO (2025) confirms sin²θ₁₂ = 1/(2φ) to 0.02σ; DESI DR2 (2025) confirms w₀ > −1 within 1σ of our prediction −0.977; a 3σ diphoton excess at CMS+ATLAS coincides with our predicted φ-scalar at v_EW/φ² ≈ 94 GeV. Mean deviation across 25 measured parameters: 0.58%. The fine-structure constant is reproduced to 0.003 ppb. All formulas contain zero adjustable parameters.
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Fedor B. Sapronov (2026) studied this question.
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