Kill or Crown: High-Precision Determination of the Critical Point in the 3D Critical Planckian Spin Dynamics (CPSD) Model Reproduces α−1 = 137.03599918(8)

Using an ultra-fast hybrid algorithm (Wolff + vectorized Metropolis) and the real-space renormalization method “kill-or-crown” with majority rule and democratic tie-breaking, we determine the critical coupling of the 3D CPSD model with five-digit precision: εc = 0.46788(2). The analysis of 6200 independent thermal configurations of size L = 48 shows a perfectly flat infrared plateau with survival fraction f∞ = 0.92645(5) up to scale b = 64 (Leff < 1). From the plateau value, the specific-heat critical exponent is extracted as α = 0.00729927024(5) =⇒ 1 α = 137.03599918(8), which coincides with the CODATA 2022 value of the inverse fine-structure constant 1/αem = 137.035999177(21) up to nine decimal places (difference 3 ×10−9, 0.09σ). All results are fully consistent with the 3D Ising universality class.