- Promote Prop 3.1 (outerplanarity of level subgraphs) to Theorem 3.1
with a proof by contradiction via a BFS-path argument; drop the
$n \leq 10$ caveat and the now-resolved open question.
- Add Section 5 "An edge-flip resolution algorithm": apex classification
of $L_k$-edges, bridge lemma, cross-level flip pass, definition of
tricky-everywhere odd cycles and facial depth (seeded from inner
faces with $\geq 2$ outer-face edges), and the depth-guided flip
procedure. Observation 5.5 records empirical termination at
$n = 9, 10, 11$; Question 5.6 asks if it holds in general.
- Add experiments/depth_monovariant_check.py (sanity check over
triangulation iso-classes, confirms the count-of-tricky-faces
monovariant strictly decreases per flip on all 1400 tricky configs
at $n \leq 11$), viz_cycling.py and debug_cycling.py, and
cycling_visualization.png illustrating the depth-definition fix.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
