# Actual character homotopy and the normal restriction

Original mathematical expression, diagram and generator are dedicated under CC0 1.0 to the extent of rights held. No external text or artwork is incorporated. The containing lesson retains the historical human credits for the ordinary Bott and inverse normal classes.

Run `python -B draw.py` with Python and Matplotlib; use `--output PATH` to select the destination. Fixed SVG salt and metadata give reproducible output. SVG contains text, neither font bytes nor glyph outlines. PNG uses installed DejaVu Sans; software and fonts retain their terms, including the existing `../FONT-NOTICE.txt`.

Panels A–D display ECH.1–ECH.10. The source point is exactly x(t)=-t/(1-t); its listed coordinates correspond to t=0,1/4,1/2,3/4. Panel B plots the fixed continuous unit coefficient v(x)=max(1-|x|,0), not a smooth core coefficient or a proof by sampling. Its exact value is max((1-2t)/(1-t),0). The homomorphism norm stays one below the zero endpoint, while every fixed source element has continuous image. The lesson proves the full reduced-algebra homotopy and original positive-dimensional disk restriction, with full coefficients retained. Vanishing of this particular class does not exclude a different normal graph class.