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

=== If you’d like to push further and try to really test whether any spherical geometry + spectrum mechanism can produce an angle close to 137.x, I recommend we do one (or more) of the following precise calculations: ===
# High-precision refractive-index run — use the full Hale & Querry / refractiveindex.info tabulated n(λ) data (interpolate the table instead of Cauchy fit). This reduces dispersion errors. (I can do this next.) PubMed<ref>{{cite web|title=PubMed|url=https://pubmed.ncbi.nlm.nih.gov/20125343/|publisher=pubmed.ncbi.nlm.nih.gov|access-date=2025-12-16}}</ref>
# Use real measured spectra — replace the Planck continuum by measured solar spectrum (ASTM or observed solar spectrum), and use real measured line intensities for the specific plasma you want to test. That gives realistic line-to-continuum contrasts.
# Parameter sweep — systematic parametric sweep: vary line amplitudes, widths, and the medium’s dispersion to map how large a line strength is needed to move the weighted mean by 0.47° (or by the amount required to match 1/α). This will tell us whether any plausible physical spectrum could do it.
# Alternative mapping (atomic-surface geometry) — don’t use water/rainbow at all. Instead try the “atomic-surface geometric mapping” you suggested: model how the electron-sphere boundary condition in QAT would map to an effective refractive index or phase shift for incoming light, then compute the equivalent “angle” or geometric factor. That would be a more direct QAT test (and might be where the golden-angle link could live).

If you want, I’ll take option (1) next and run the same calculation but using the tabulated Hale & Querry data (or the refractiveindex.info page) and a solar spectrum + the atomic lines we discussed. That will be the most direct, higher-precision check. Would you like me to do that now?