check_owr4798013_run2.py (second independent verification run, AI-assisted)
(A) Lemma 3.1: explicit collapse B(i,d) -> C*_{i+1}, every step an elementary collapse
  (i,d)=(0,2): ok, 2 elementary collapses, 2 faces left (C*_1)
  (i,d)=(0,3): ok, 6 elementary collapses, 2 faces left (C*_1)
  (i,d)=(1,3): ok, 8 elementary collapses, 8 faces left (C*_2)
  (i,d)=(0,4): ok, 14 elementary collapses, 2 faces left (C*_1)
  (i,d)=(1,4): ok, 28 elementary collapses, 8 faces left (C*_2)
  (i,d)=(2,4): ok, 26 elementary collapses, 26 faces left (C*_3)
  (i,d)=(0,5): ok, 30 elementary collapses, 2 faces left (C*_1)
  (i,d)=(1,5): ok, 76 elementary collapses, 8 faces left (C*_2)
  (i,d)=(2,5): ok, 98 elementary collapses, 26 faces left (C*_3)
  (i,d)=(3,5): ok, 80 elementary collapses, 80 faces left (C*_4)
  (i,d)=(0,6): ok, 62 elementary collapses, 2 faces left (C*_1)
  (i,d)=(1,6): ok, 188 elementary collapses, 8 faces left (C*_2)
  (i,d)=(2,6): ok, 290 elementary collapses, 26 faces left (C*_3)
  (i,d)=(3,6): ok, 312 elementary collapses, 80 faces left (C*_4)
  (i,d)=(4,6): ok, 242 elementary collapses, 242 faces left (C*_5)
  (i,d)=(0,7): ok, 126 elementary collapses, 2 faces left (C*_1)
  (i,d)=(1,7): ok, 444 elementary collapses, 8 faces left (C*_2)
  (i,d)=(2,7): ok, 786 elementary collapses, 26 faces left (C*_3)
  (i,d)=(3,7): ok, 968 elementary collapses, 80 faces left (C*_4)
  (i,d)=(4,7): ok, 958 elementary collapses, 242 faces left (C*_5)
  (i,d)=(5,7): ok, 728 elementary collapses, 728 faces left (C*_6)
  (i,d)=(0,8): ok, 254 elementary collapses, 2 faces left (C*_1)
  (i,d)=(1,8): ok, 1020 elementary collapses, 8 faces left (C*_2)
  (i,d)=(2,8): ok, 2034 elementary collapses, 26 faces left (C*_3)
  (i,d)=(3,8): ok, 2776 elementary collapses, 80 faces left (C*_4)
  (i,d)=(4,8): ok, 3046 elementary collapses, 242 faces left (C*_5)
  (i,d)=(5,8): ok, 2900 elementary collapses, 728 faces left (C*_6)
  (i,d)=(6,8): ok, 2186 elementary collapses, 2186 faces left (C*_7)
  (i,d)=(0,9): ok, 510 elementary collapses, 2 faces left (C*_1)
  (i,d)=(1,9): ok, 2300 elementary collapses, 8 faces left (C*_2)
  (i,d)=(2,9): ok, 5106 elementary collapses, 26 faces left (C*_3)
  (i,d)=(3,9): ok, 7640 elementary collapses, 80 faces left (C*_4)
  (i,d)=(4,9): ok, 9030 elementary collapses, 242 faces left (C*_5)
  (i,d)=(5,9): ok, 9332 elementary collapses, 728 faces left (C*_6)
  (i,d)=(6,9): ok, 8730 elementary collapses, 2186 faces left (C*_7)
  (i,d)=(7,9): ok, 6560 elementary collapses, 6560 faces left (C*_8)
  (i,d)=(0,10): ok, 1022 elementary collapses, 2 faces left (C*_1)
  (i,d)=(1,10): ok, 5116 elementary collapses, 8 faces left (C*_2)
  (i,d)=(2,10): ok, 12530 elementary collapses, 26 faces left (C*_3)
  (i,d)=(3,10): ok, 20440 elementary collapses, 80 faces left (C*_4)
  (i,d)=(4,10): ok, 25862 elementary collapses, 242 faces left (C*_5)
  (i,d)=(5,10): ok, 28180 elementary collapses, 728 faces left (C*_6)
  (i,d)=(6,10): ok, 28250 elementary collapses, 2186 faces left (C*_7)
  (i,d)=(7,10): ok, 26224 elementary collapses, 6560 faces left (C*_8)
  (i,d)=(8,10): ok, 19682 elementary collapses, 19682 faces left (C*_9)
  pairs checked: 45
(B) Klee-Novik Lemma 3.5: shelling of the stars of x_d and y_d with restrictions Sel(tau)
  d=2: i=0..0: ok
  d=3: i=0..1: ok
  d=4: i=0..2: ok
  d=5: i=0..3: ok
  d=6: i=0..4: ok
  d=7: i=0..5: ok
  d=8: i=0..6: ok
(C) Lemma 3.3 and (D) all vertices of C*_d in the boundary of B(i,d)
  (i,d)=(0,2): Lemma 3.3 ok (4 boundary ridges); every vertex in the boundary: True
  (i,d)=(0,3): Lemma 3.3 ok (6 boundary ridges); every vertex in the boundary: True
  (i,d)=(1,3): Lemma 3.3 ok (6 boundary ridges); every vertex in the boundary: True
  (i,d)=(0,4): Lemma 3.3 ok (8 boundary ridges); every vertex in the boundary: True
  (i,d)=(1,4): Lemma 3.3 ok (16 boundary ridges); every vertex in the boundary: True
  (i,d)=(2,4): Lemma 3.3 ok (8 boundary ridges); every vertex in the boundary: True
  (i,d)=(0,5): Lemma 3.3 ok (10 boundary ridges); every vertex in the boundary: True
  (i,d)=(1,5): Lemma 3.3 ok (30 boundary ridges); every vertex in the boundary: True
  (i,d)=(2,5): Lemma 3.3 ok (30 boundary ridges); every vertex in the boundary: True
  (i,d)=(3,5): Lemma 3.3 ok (10 boundary ridges); every vertex in the boundary: True
  (i,d)=(0,6): Lemma 3.3 ok (12 boundary ridges); every vertex in the boundary: True
  (i,d)=(1,6): Lemma 3.3 ok (48 boundary ridges); every vertex in the boundary: True
  (i,d)=(2,6): Lemma 3.3 ok (72 boundary ridges); every vertex in the boundary: True
  (i,d)=(3,6): Lemma 3.3 ok (48 boundary ridges); every vertex in the boundary: True
  (i,d)=(4,6): Lemma 3.3 ok (12 boundary ridges); every vertex in the boundary: True
  (i,d)=(0,7): Lemma 3.3 ok (14 boundary ridges); every vertex in the boundary: True
  (i,d)=(1,7): Lemma 3.3 ok (70 boundary ridges); every vertex in the boundary: True
  (i,d)=(2,7): Lemma 3.3 ok (140 boundary ridges); every vertex in the boundary: True
  (i,d)=(3,7): Lemma 3.3 ok (140 boundary ridges); every vertex in the boundary: True
  (i,d)=(4,7): Lemma 3.3 ok (70 boundary ridges); every vertex in the boundary: True
  (i,d)=(5,7): Lemma 3.3 ok (14 boundary ridges); every vertex in the boundary: True
  (i,d)=(0,8): Lemma 3.3 ok (16 boundary ridges); every vertex in the boundary: True
  (i,d)=(1,8): Lemma 3.3 ok (96 boundary ridges); every vertex in the boundary: True
  (i,d)=(2,8): Lemma 3.3 ok (240 boundary ridges); every vertex in the boundary: True
  (i,d)=(3,8): Lemma 3.3 ok (320 boundary ridges); every vertex in the boundary: True
  (i,d)=(4,8): Lemma 3.3 ok (240 boundary ridges); every vertex in the boundary: True
  (i,d)=(5,8): Lemma 3.3 ok (96 boundary ridges); every vertex in the boundary: True
  (i,d)=(6,8): Lemma 3.3 ok (16 boundary ridges); every vertex in the boundary: True
  (i,d)=(0,9): Lemma 3.3 ok (18 boundary ridges); every vertex in the boundary: True
  (i,d)=(1,9): Lemma 3.3 ok (126 boundary ridges); every vertex in the boundary: True
  (i,d)=(2,9): Lemma 3.3 ok (378 boundary ridges); every vertex in the boundary: True
  (i,d)=(3,9): Lemma 3.3 ok (630 boundary ridges); every vertex in the boundary: True
  (i,d)=(4,9): Lemma 3.3 ok (630 boundary ridges); every vertex in the boundary: True
  (i,d)=(5,9): Lemma 3.3 ok (378 boundary ridges); every vertex in the boundary: True
  (i,d)=(6,9): Lemma 3.3 ok (126 boundary ridges); every vertex in the boundary: True
  (i,d)=(7,9): Lemma 3.3 ok (18 boundary ridges); every vertex in the boundary: True
  (i,d)=(0,10): Lemma 3.3 ok (20 boundary ridges)
  (i,d)=(1,10): Lemma 3.3 ok (160 boundary ridges)
  (i,d)=(2,10): Lemma 3.3 ok (560 boundary ridges)
  (i,d)=(3,10): Lemma 3.3 ok (1120 boundary ridges)
  (i,d)=(4,10): Lemma 3.3 ok (1400 boundary ridges)
  (i,d)=(5,10): Lemma 3.3 ok (1120 boundary ridges)
  (i,d)=(6,10): Lemma 3.3 ok (560 boundary ridges)
  (i,d)=(7,10): Lemma 3.3 ok (160 boundary ridges)
  (i,d)=(8,10): Lemma 3.3 ok (20 boundary ridges)
ALL CHECKS PASSED: True   (4.2 s)
