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

=== (implemented numerically; I can show the code & plot if you want) ===
# I approximated the Sun by a black-body (Planck) spectrum at T=5778 KT = 5778\ \mathrm{K}T=5778 K. This is a common first approximation to the solar spectral shape (it’s not a perfect match to measured solar flux, but it’s good for exploratory tests).
# I used a simple geometric phase mapping (one plausible, physically-motivated choice):

ϕ(λ;reff)  =  360∘×frac⁡ ⁣(2π reffλ)\phi(\lambda; r_\text{eff}) \;=\; 360^\circ \times \operatorname{frac}\!\bigg(\frac{2\pi\,r_\text{eff}}{\lambda}\bigg)ϕ(λ;reff)=360∘×frac(λ2πreff)
Interpretation: 2πreffλ\dfrac{2\pi r_\text{eff}}{\lambda}λ2πreff is the number of wavelengths that fit around the sphere’s circumference; the fractional part gives the leftover phase (a number in [0,1)[0,1)[0,1)) and multiplying by 360∘360^\circ360∘ converts to a geometric angle. This is a straightforward way of turning a wavelength into a spherical boundary angle.
# I used reff=a0/2r_\text{eff} = a_0/2reff=a0/2 as the “half-Bohr-radius” geometry you proposed (where a0a_0a0 is the Bohr radius), and I computed the Planck-weighted mean of ϕ(λ)\phi(\lambda)ϕ(λ) across a λ-grid from 1 nm → 2000 nm (UV → near-IR) using the Planck weighting Bλ(T)B_\lambda(T)Bλ(T).
# I then inverted the same mapping to find what radius reffr_\text{eff}reff would be required so that the Planck-weighted mean angle equals the golden-angle value 137.507764…∘137.507764\ldots^\circ137.507764…∘ (and also did the very close value 137.035999…° for comparison).