(E) Lemma 4: 300 random trees (h<=40): domain size 2h-1, surjective, consecutive equal/adjacent: OK
(S) Lemma 5 tube walk <= c_d (n^(1-1/d)+1) L on 400 sets per d (n<=300): OK; max length/bound by d: {1: 0.49, 2: 0.281, 3: 0.133, 4: 0.063}
(F1) explicit box path of (ii): every step literally legal, growth length d(n-1)L, F inside the top box: [(2, 2, 4), (2, 3, 12), (3, 2, 12), (2, 4, 24)]
(F2) literal BFS, (d,n)=(2,2), L=2: polytopes=36, TP(x,F,x)=8, TP(x,F,y)=8 (claimed 2d(n-1)L=8)
(F2) literal BFS, (d,n)=(2,3), L=3: polytopes=784, TP(x,F,x)=24, TP(x,F,y)=24 (claimed 2d(n-1)L=24)
(F3)  d n  L  N   TP+N  TS(x,F,x)  TS+N  n^(2d-1)  (2d+1)n^d  log(TP+N)/log(TS+N)  d/(2d-1)
      2 2  2   4    12         8     12        8        20   1.0000              0.6667
      2 3  3   9    33        30     39       27        45   0.9544              0.6667
      2 4  4  16    64        64     80       64        80   0.9491              0.6667
      3 2  4   8    32        32     40       32        56   0.9395              0.6000
      4 2  8  16    80       128    144      128       144   0.8817              0.5714
ALL CHECKS PASSED
