Add level resolutions of maximal planar graphs paper

Migrate the paper content into the amsart template and include the supporting experiments scripts.
2026-05-19 23:35:01 -04:00
parent 5b0a5b290a
commit bd9c46d3e4
31 changed files with 5492 additions and 0 deletions
@@ -0,0 +1,58 @@
+# Level Resolution Experiments
+
+Computational investigation of a structural proof strategy for the four
+color theorem via *level resolutions* of maximal planar graphs.
+
+See `paper.tex` for full definitions, conjectures, and findings.
+
+## Files
+
+### Core library
+- `level_cycles.py` — levels, level subgraphs, level cycles, resolution
+  enumeration (used by old-definition coverage).
+- `triangulation_gen.py` — vertex-insertion + flip closure (good to n=10).
+- `triangulation_gen_fast.py` — WL-hash pre-filter for n ≥ 11.
+- `balanced_layout.py` — Tutte-init random-search planar layout.
+- `four_color.py` — level 4-coloring via parity 2-coloring of L_k.
+
+### Experiments
+- `coverage_new_def.py` — **coverage under the cleaner definition**:
+  G' is a level resolution of G via S iff its parity subgraphs are
+  bipartite. Reachability reduces to "G' admits a bipartite 2-partition
+  with cardinality matching some BFS-realizable parity split."
+- `coverage.py`, `coverage_fast.py`, `coverage_chunked.py` — coverage
+  under the OLD (stricter) definition involving specific edge flips on
+  level cycles.
+- `face_counting.py` — per-target preimage counts (N_iso, N_paths) under
+  the old definition.
+- `orbit_check.py` — orbit-counting with k-flip reverse-preimages (used
+  for old-definition icosahedron analysis).
+
+### Visualizations
+- `plot_oct.py`, `n7_examples.py`, `four_color_viz.py`.
+
+## Summary under the new definition
+
+| n  | iso-classes | reachable | md4 reachable |
+|----|-------------|-----------|---------------|
+| 6  | 2           | 2         | 1/1           |
+| 7  | 5           | 5         | 1/1           |
+| 8  | 14          | 14        | 2/2           |
+| 9  | 50          | 50        | 5/5           |
+| 10 | 233         | 233       | 12/12         |
+| 11 | 1249        | 1249      | 34/34         |
+| 12 | icosahedron | reachable | yes           |
+
+**Every iso-class is reachable** at every tested size. The previously
+"uncovered" classes T1 (n=7) and T6 (n=8) under the old definition are
+both reachable under the cleaner definition.
+
+The new definition makes coverage equivalent to 4CT plus a BFS-realizable
+partition cardinality constraint, raising the question of what additional
+structure on the preimage G would make the framework non-circular.
+
+## Dependencies
+
+```
+pip install networkx matplotlib numpy scipy
+```