[fatbrowndog]

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.

[albert_roca]

It's not circular. It rearranges into a standard quadratic equation: x^2 − 24Sx + 24 = 0. α is derived as the root of this equation.

[fatbrowndog]

α⁻¹ = S - 1/(24α) α⁻¹·24α = 24αS - 1 24α²S - 24α - 1 = 0

α = (24 ± √(576 + 96S))/(48S) α = (24 + √(576 + 96·137.036...))/(48·137.036...) α = (24 + √13,723.66...)/(6577.74...) α = (24 + 117.12...)/(6577.74...) α = 141.12.../6577.74... α ≈ 0.021454...

α⁻¹ ≈ 46.61 ??? That's wrong!

[fatbrowndog]

α⁻¹ = S - 1/(24α)

α⁻¹·24α = 24αS - 1

24α²S - 24α - 1 = 0

α = (24 ± √(576 + 96S))/(48S)

α = (24 + √(576 + 96·137.036...))/(48·137.036...)

α = (24 + √13,723.66...)/(6577.74...)

α = (24 + 117.12...)/(6577.74...)

α = 141.12.../6577.74...

α ≈ 0.021454...

α⁻¹ ≈ 46.61 ???

That's wrong!

[fatbrowndog]

Doesn't fix or predict Fan et al. 2024 latest dataset.

Try harder.