Add Even Level Graph Generators paper + extend Level Switching reachability

- New paper papers/even_level_graph_generators/: defines Even Level
  Graph (every level cycle even), derived level graphs, intertwining
  trees, and the disjunction conjecture (every maximal planar graph is
  a derived level graph or intertwining tree). Empirically tested
  through n=11: every iso class is at least an intertwining tree, so
  the disjunction holds trivially in this range. The intertwining tree
  disjunct fails at the Tutte graph dual (n=25), so the disjunction
  becomes non-trivial past some unknown threshold.

- Level Switching paper: adds Section 4 (Reachability via edge
  switches) with the two-step argument (Sleator-Tarjan-Thurston for
  Case 1; face-merges for Case 2) and Theorem 4.1 (O(n) edge switches
  suffice to reach all-depth-0).

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

papers/even_level_graph_generators/experiments/plot_counterexample.py

@@ -0,0 +1,38 @@
+"""Plot iso[49] at n=9, the counterexample to Conjecture 4.4."""
+import sys
+import os
+sys.path.insert(0, '/Users/didericis/Code/math-research/papers/'
+                'level_resolutions_of_maximal_planar_graphs/experiments')
+import networkx as nx
+import matplotlib.pyplot as plt
+from triangulation_gen import enumerate_all_triangulations
+
+OUT_DIR = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))
+
+tris = enumerate_all_triangulations(9)
+G = tris[49]
+print(f'iso[49] degree sequence: {sorted([G.degree(v) for v in G.nodes()], reverse=True)}')
+print(f'iso[49] edges: {sorted(G.edges())}')
+
+# Use planar layout
+_, emb = nx.check_planarity(G)
+pos = nx.combinatorial_embedding_to_pos(emb)
+
+fig, ax = plt.subplots(figsize=(8, 7))
+nx.draw_networkx_edges(G, pos, ax=ax, edge_color='#333', width=1.5)
+# Color vertices by degree
+degree_color = {4: '#3b82f6', 5: '#dc2626'}
+node_colors = [degree_color[G.degree(v)] for v in G.nodes()]
+nx.draw_networkx_nodes(G, pos, ax=ax, node_color=node_colors,
+                       node_size=600, edgecolors='black', linewidths=1.2)
+nx.draw_networkx_labels(G, pos, ax=ax, font_color='white',
+                        font_size=11, font_weight='bold')
+ax.set_aspect('equal'); ax.axis('off')
+ax.set_title('iso[49] at $n=9$: degree sequence (5,5,5,5,5,5,4,4,4).\n'
+             'NOT a valid derived level graph of any Even Level Graph.\n'
+             'Blue = degree 4, Red = degree 5.', fontsize=11)
+fig.tight_layout()
+out = os.path.join(OUT_DIR, 'fig_n9_counterexample.png')
+fig.savefig(out, dpi=180, bbox_inches='tight')
+plt.close(fig)
+print(f'wrote {out}')