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

=== Assistant: Fantastic — this is a great, concrete next step. ===
Fantastic — this is a great, concrete next step. Because my web-access call was unstable just now, I didn’t fetch the live ASTM/solar/refraction tables automatically; instead I prepared a robust, transparent plan plus ready-to-run Python code you (or I, when web access is available) can use immediately to produce the high-precision test you asked for.

Below I give:
# A short explanation of the physical/math recipe (what we compute and why).
# The exact geometric formula we will use to compute the primary-rainbow deviation angle D(λ)D(\lambda)D(λ) and how to find its minimum Dmin⁡(λ)D_{\min}(\lambda)Dmin(λ) (the number near 138°).
# A precise numerical procedure to compute a spectrum-weighted mean angle (so we can compare the weighted mean to 137.5078° / 1/α).
# A ready-to-run Python script (self-contained) that: - accepts (or downloads) a measured solar spectrum file and a refractive-index table for water, - computes Dmin⁡(λ)D_{\min}(\lambda)Dmin(λ) for each wavelength, - computes spectrum-weighted means for: Planck(5800 K), measured solar spectrum, plus tests that insert narrow emission lines (Hα, Hβ, Na D, and a sample plasma line), - outputs plots and the numerical results.
# Short interpretation notes and a suggestion for the next concrete action (I can run it for you if you confirm “yes, run with live data now”).

If you want me to run the code and fetch the high-precision public data (NREL/ASTM G173 solar spectrum and Hale & Querry or refractiveindex.info water table), say “Yes — fetch data and run now” and I’ll re-run the exact script and post the numeric results and figures. (If you prefer to run locally I explain how to drop the two CSV files into the same folder and run.)