Stress-tests the iterated preprocessing algorithm on random
maximal-outerplanar triangulations: terminates on n<=60 within bounded
steps, occasionally hits step cap at n=80 with random edge choice.
Scaffolds the user-proposed v_c-rotation algorithm and documents the
monovariant findings (lexicographic depth signature is weakly but not
strictly decreasing under preprocessing).
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
Add 21-vertex and 24-vertex examples showing recursive lopsidedness
at d=2. Empirically confirm that the iterated algorithm (balanced
switch when available, preprocess otherwise) drives every face to
depth 0 on all tested configurations. Frame the remaining open
question as identifying a strictly-decreasing monovariant under
unbalanced preprocessing switches.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
Defines level cycles, edge switches, surface switches, and facial depth
on level components of plane triangulations. Proves outerplanarity of
level components and a depth-descent lemma. Introduces balanced surface
switches and proves they remove a depth-d level cycle while creating
1-2 new depth-(d-1) cycles. Documents the 9-vertex counterexample where
no balanced switch exists and sketches preprocessing toward
balancedness, leaving general termination open.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
didericis