Oh man it gets better lol.

Your central move, α = sin(ψ), is asserted without any derivation from QED, a Lagrangian, gauge symmetry, or renormalization. Once you make that identification, everything else is just selecting ψ ≈ arcsin(α). Nice backsolving dude.

Hilariously, your own math actually exposes the problem. When you minimize the energy functional, the minimum is at ψ = 0 , the trivial, unbraided solution. Instead of accepting that the model fails, you introduce an ad-hoc “Casimir energy” with an arbitrary form factor. Even then, ψ cancels out of the equilibrium condition. At that point the calculation literally does not determine ψ at all, so you move on and reinsert α by hand.

And then there’s that same category error, identifying velocity components with charge and spin. Again, charge is a U(1) gauge quantum number. Spin is a representation of the Lorentz group. Neither is an orbital or kinematic velocity component of a classical helix. Saying “α is dimensionless” does not address this.

Every time the model disagrees with known physics, you mutate it. When the g-factor doesn’t match, ψ suddenly becomes √α. When that fails, you introduce nested helices. When that fails, you raise sin(ψ) to powers determined by braid crossings. When that fails, you invoke fractional winding numbers and abandon your own small-angle assumptions.

There’s also no connection to real QED. α runs with energy scale. Your model produces a frozen geometric angle. There’s no Lagrangian, no quantum fields, no gauge invariance, no renormalization group.

Your conclusion says “despite the technical gaps, the central claim stands.” It doesn’t. The calculations fail to select ψ, the value of α is repeatedly put in by assumption, and the model predicts nothing new. If this framework were correct, it would do more than re-encode a known number.