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

=== - QAT emphasizes spherical geometry and links constants to geometry. The calculation shows that observed or effective angular numbers that come from spherical optical processes depend not only on the geometry and refractive index, but also on the spectrum (which wavelengths carry the energy) and on how scattering amplitude selects wavelengths (Mie / droplet size). ===
* The small offset between the golden angle (≈137.5078°) and inverse fine structure (≈137.036) is about 0.47°. In our geometric/spectral calculation a shift of that order is well within the range produced by changing the effective source spectrum (e.g., moving from a 5800 K blackbody to a ≈3800 K blackbody shifts the weighted mean by roughly that much). So spectral weighting is a plausible mechanism to produce small angular offsets — but it’s not a proof that the fine-structure number comes from rainbow geometry.
* Two important caveats: 1. I used a Sellmeier-style n(λ)n(\lambda)n(λ) fit (standard and good across the visible band) — but precise constants and temperature dependence of nnn will change numbers slightly. 2. I did not include Mie scattering amplitude, interference (supernumerary bows), droplet-size distribution, polarization or atmospheric effects. Those interact strongly with intensity vs angle and can move the visually perceived center of a bow by up to a few tenths of a degree in realistic conditions. To make a firm link to a constant like α you must include the full scattering physics (Mie) and measured spectra.