Refactor canonical_coloring into coloring_skeleton (phase-independent parts) +
canonical_coloring_explicit (explicit phases + DFS colour order) + a random-phase
wrapper for back-compat. This exposes the two control knobs deterministically so
they can be enumerated rather than only sampled.
Add a fully worked example on the smallest clean graph (ring [3,5]+hub, 9
vertices, one odd seam, no gadgets): even_program_walkthrough.md traces all six
stages -- generate G with embedding, pick source + BFS levels, choose the diamond
site that evens the level-5 seam, build M(G'), the canonical colouring (seam
mono-3, hub annulus alternates, root by DFS), and a real {1,2}-Kempe switch that
makes the diamond quad reducible. dump_walkthrough.py reproduces every number;
draw_walkthrough.py renders the 4-panel figure even_program_walkthrough.png.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
didericis
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