# The split reduced germ algebra and disk nullhomotopy

Original mathematical expression, diagrams and generator: CC0 1.0 to the extent rights exist. No externally authored artwork or source text is incorporated. The lesson retains its human mathematical credits. Fonts and software retain their terms, including ../FONT-NOTICE.txt.

Run python -B draw.py with Python and Matplotlib. It writes two PNG/SVG pairs under figures. Fixed SVG salt and metadata permit byte-exact replay in the recorded environment. SVG contains text without embedded fonts or font glyph outlines.

The first figure gives exact circle coordinate angle=2 arctan(x), the actual positive source fibres and negative unit fibres, endpoint isotropy, and the bound (sqrt(3)/2)^n from SGD.6--SGD.11. The second uses the exact smooth argument theta(t)=2*pi*H(t-1/4)/(H(t-1/4)+H(3/4-t)), with H(s)=exp(-1/s) for s>0 and zero otherwise, and displays SGD.12--SGD.16 for s=1/4,1/2,3/4,1. Neither diagram samples the unspecified Baire-selected diffeomorphisms. Their existence and all-word germ faithfulness are proved in Lemmas11CM.1--2.