his formula: α⁻¹ = (4π³ + π² + π) - (α/24)

α⁻¹ = 137.0359996 Experimental (CODATA): 137.0359991 Δ: < 0.005 ppm

Critical Problem: This is CIRCULAR The formula is: α⁻¹ = S - (α/24)

But α appears on both sides! This is not a closed-form solution. To solve it, you need: α⁻¹ = S - (α/24) α⁻¹ + α/24 = S α⁻¹(1 + 1/(24·α⁻¹)) = S This requires knowing α already to solve for α. It's circular.