Restate conjecture with "bridge-derived"; update empirical table and n=21

- Conjecture now reads "bridge-derived level graph ... an intertwining tree,
  or both" -- the stronger form the evidence actually supports (a bridge-
  derived level graph is automatically a valid derived level graph).
- Empirical table recomputed for bridge-derivability, exhaustively for n<=9
  (every backward bridge-orbit fully enumerable there):
    n=7: 1 inter-only; n=8: 2 inter-only; n=9: 14 inter-only; missing=0.
  Added prose: below n=21 every class is intertwining, so the table shows
  how far the bridge-derived disjunct reaches on its own (36/50 at n=9) and
  that the two disjuncts complement each other; "bridge only" is 0 in range.
- n=21 subsection notes the four witnesses are explicit, short (path lengths
  3,1,2,4), archived, and step-verified.

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

papers/even_level_graph_generators/experiments/recompute_table.py

@@ -0,0 +1,37 @@
+"""Recompute the empirical table for the bridge-derived disjunction:
+for each n, count iso classes that are bridge-derived only / intertwining
+only / both / neither (missing)."""
+import sys
+import os
+sys.path.insert(0, '/Users/didericis/Code/math-research/papers/'
+                'level_resolutions_of_maximal_planar_graphs/experiments')
+sys.path.insert(0, os.path.dirname(os.path.abspath(__file__)))
+from triangulation_gen import enumerate_all_triangulations
+from small_n_probe import is_bridge_derived
+from test_disjunction import is_intertwining_tree
+
+
+def main(ns):
+    print('n  iso  bridge_only  inter_only  both  missing', flush=True)
+    for n in ns:
+        tris = enumerate_all_triangulations(n)
+        bo = io = both = miss = 0
+        for G in tris:
+            bd = is_bridge_derived(G)
+            it = is_intertwining_tree(G)
+            if isinstance(it, tuple):
+                it = it[0]
+            if bd and it:
+                both += 1
+            elif bd:
+                bo += 1
+            elif it:
+                io += 1
+            else:
+                miss += 1
+        print(f'{n} {len(tris)} {bo} {io} {both} {miss}', flush=True)
+
+
+if __name__ == '__main__':
+    ns = [int(x) for x in sys.argv[1:]] or [6, 7, 8, 9, 10, 11, 12]
+    main(ns)