Reproducing the elliptic example figures

The elliptic example lesson contains the proofs, exact inequalities and six rational sample rows illustrated by these figures. The retained original plotting source uses historical generic output names and a historical ../draft.md proof locator in its explanatory text; it does not read that file. In this reader, the corresponding proof is the linked lesson.

With Python, NumPy, SymPy and Matplotlib installed, run python figures/reproduce-an02-l107-figures.py from the course directory. The wrapper copies the exact retained source under its expected basename make_figures.py into a new figures/an02-l107-reproduced folder, then runs its exact algebra checks and plotting functions there. That output folder must not already exist. Original reader assets remain unchanged.

The source writes threshold-regions.png, scale-intervals.png, their SVG versions, and figure-validation.json. The wrapper also copies these generated outputs under the reader names an02-l107-elliptic-threshold-regions.png, an02-l107-elliptic-scale-intervals.png, the corresponding SVG names, and an02-l107-elliptic-figure-validation.json, in the same output folder. The original six rational cases and symbolic identities are the mathematical checks; generated SVG identifiers and file hashes can depend on the plotting environment.

The plots show the stated parameter crops, strict thresholds, included order boundaries and selected rational scale intervals. They do not depict the infinite assembled smooth solution. Original expression, figures and wrapper: GPT-6.1 Sol (OpenAI), Ultra; CC0.