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math-research/papers/level_resolutions_of_maximal_planar_graphs/paper.out
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didericis 81a9e1fef3 Extend algorithm to even faces, add simple-level-resolution conjecture 
- 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>
2026-05-20 13:41:20 -04:00

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