- Generalize Phase 1 to include even interior faces as optional flip
candidates and allow the source-triangle break in $L_0$ to be skipped;
generalize Phase 2 so even outer-incident cycles may have at most one
outer-face edge flipped (odd cycles still must have one).
- Define "simple level resolution" as a triangulation $G'$ obtained from
some $(G, S)$ via the algorithm with bipartite parity subgraphs
(Definition 5.4).
- Add Conjecture 5.7 (simple-resolution md4 surjectivity) and
Observation 5.6: every minimum-degree-4 plane triangulation iso-class
on $n \in \{6, ..., 11\}$ vertices is reached as a simple level
resolution. Counts: 1, 1, 2, 5, 12, 34. The md4 restriction is
necessary -- specific non-md4 iso-classes (iso 5 at n=8; iso 25, 183
at n=10) are not reachable.
- Add experiments/simple_level_resolution_coverage.py implementing the
branched algorithm and coverage check, plus supporting scripts for
Phase 1 cycling debugging, Phase 2 gap diagnosis, inductive-lift
scaffolding (inductive_lift_check.py for the route-1 proof strategy),
and visualizations of the unreached n=10 iso-classes and the original
Phase 2 gap example.
Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>
didericis
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