Editing Openai/6897769e-4ee4-800f-aba5-69cca34f701c (section)

=== Not under this particular geometric phase mapping. The numbers show the golden-angle appears when the sphere size and photon wavelength have the particular ratio needed to give a fractional cycle ≈ 0.381966… — that ratio is roughly r/λ≈0.0608r/\lambda \approx 0.0608r/λ≈0.0608. For visible light (λ ~ 400–700 nm) that forces r into tens of nanometres, not atomic scale. ===

That doesn’t mean your broader QAT idea is dead — it means:
* If QAT claims the golden-angle and α are both geometric consequences at the same microscopic scale, then a single simple circumference-phase mapping with optical photons and the Bohr radius does not reproduce it.
* But if QAT allows the relevant geometry to come from a different effective radius (e.g., nanoparticle-sized boundaries, or collective plasma structures, or very-short wavelength photons interacting with atomic radii), then spherical geometry can produce angles near the golden-angle. In other words: the scale matters.