Two illustrations in boundary_cut_tire.tex:
1. Thick H_1 case: hexagonal H_1 with 3 OUT pendants (outward,
dashed red) and 3 IN pendants (inward, dashed green). Shows
T_∂ cycle as the hexagon boundary between low-side outer
region (red shade) and high-side inner region (green shade).
2. Thin H_1 case: H_1 = path of 3 edges (tree), single face is
f_∂, boundary walk traverses each edge twice (gray arrows
showing the two-sided traversal). 2 OUT pendants at V_{deg=2}
vertices, no IN pendants. This is the dodecahedron cut #0
side 0 structure where the high-side-only DP failed.
Note grows from 3 to 4 pages.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
didericis
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