==============================================================================
PART F. DV21 Table 1 'symdim' (non-generic = CDS-generic pentagonal bipyramid)
  cell: base [(-9, -6), (15, -3), (12, 9), (3, 15), (-4, 5)] apices (0, -3, 3) (-1, -3, -3)
   r=1 k=2..9: computed [7, 16, 36, 66, 106, 156, 216, 286]
                 DV21     [7, 16, 36, 66, 106, 156, 216, 286]
   r=2 k=3..11: computed [11, 18, 32, 57, 92, 137, 192, 257, 332]
                 DV21     [11, 18, 32, 57, 92, 137, 192, 257, 332]
   r=3 k=4..12: computed [16, 24, 34, 51, 80, 120, 170, 230, 300]
                 DV21     [16, 24, 34, 51, 80, 120, 170, 230, 300]
   r=4 k=5..13: computed [22, 31, 42, 56, 78, 112, 157, 212, 277]
                 DV21     [22, 31, 42, 56, 78, 112, 157, 212, 277]
  cell: base [(3, -9), (6, 8), (4, 6), (-2, 10), (-5, 1)] apices (3, 2, 4) (-1, -2, -2)
   r=1 k=2..9: computed [7, 16, 36, 66, 106, 156, 216, 286]
                 DV21     [7, 16, 36, 66, 106, 156, 216, 286]
   r=2 k=3..11: computed [11, 18, 32, 57, 92, 137, 192, 257, 332]
                 DV21     [11, 18, 32, 57, 92, 137, 192, 257, 332]
   r=3 k=4..12: computed [16, 24, 34, 51, 80, 120, 170, 230, 300]
                 DV21     [16, 24, 34, 51, 80, 120, 170, 230, 300]
   r=4 k=5..13: computed [22, 31, 42, 56, 78, 112, 157, 212, 277]
                 DV21     [22, 31, 42, 56, 78, 112, 157, 212, 277]
  (values for r>=2 computed exactly over Q up to k=10, mod p=2147483647 above)
==============================================================================
PART G. Euler characteristic chi(R/J,k) of the BSS complex vs the OWR lower bound
  n=3 m=3 chi(k),k<=7 = [1, 3, 6, 12, 24, 42, 66, 96] ; sum_{k<=d} chi, d=2..7 = [10, 22, 46, 88, 154, 250] ; OWR LB = [10, 22, 46, 88, 154, 250] ; H-chi = [0, 0, 1, 1, 0, 0, 0, 0]
  n=4 m=2 chi(k),k<=7 = [1, 3, 7, 16, 32, 56, 88, 128] ; sum_{k<=d} chi, d=2..7 = [11, 27, 59, 115, 203, 331] ; OWR LB = [11, 27, 59, 115, 203, 331] ; H-chi = [0, 0, 0, 1, 1, 0, 0, 0]
  n=4 m=3 chi(k),k<=7 = [1, 3, 6, 14, 30, 54, 86, 126] ; sum_{k<=d} chi, d=2..7 = [10, 24, 54, 108, 194, 320] ; OWR LB = [10, 24, 54, 108, 194, 320] ; H-chi = [0, 0, 1, 1, 0, 0, 0, 0]
  n=4 m=4 chi(k),k<=7 = [1, 3, 6, 14, 30, 54, 86, 126] ; sum_{k<=d} chi, d=2..7 = [10, 24, 54, 108, 194, 320] ; OWR LB = [10, 24, 54, 108, 194, 320] ; H-chi = [0, 0, 1, 0, 0, 0, 0, 0]
  n=5 m=5 chi(k),k<=7 = [1, 3, 6, 16, 36, 66, 106, 156] ; sum_{k<=d} chi, d=2..7 = [10, 26, 62, 128, 234, 390] ; OWR LB = [10, 26, 62, 128, 234, 390] ; H-chi = [0, 0, 1, 0, 0, 0, 0, 0]
  n=6 m=3 chi(k),k<=7 = [1, 3, 6, 18, 42, 78, 126, 186] ; sum_{k<=d} chi, d=2..7 = [10, 28, 70, 148, 274, 460] ; OWR LB = [10, 28, 70, 148, 274, 460] ; H-chi = [0, 0, 1, 1, 0, 0, 0, 0]
  n=7 m=4 chi(k),k<=7 = [1, 3, 6, 20, 48, 90, 146, 216] ; sum_{k<=d} chi, d=2..7 = [10, 30, 78, 168, 314, 530] ; OWR LB = [10, 30, 78, 168, 314, 530] ; H-chi = [0, 0, 1, 0, 0, 0, 0, 0]
==============================================================================
PART H. Lemma 2.1 on random planar fans (orders constant on lines), exact
  Lemma 2.1: 540 (fan, degree) comparisons, mismatches so far 0
==============================================================================
PART I. Formula-level checks
  Cor 1.2 checked on 37284 triples (3<=n<=60, admissible m, 2<=d<=40)
  Table 2 entries checked
  Thm 4.2 derivation formulas agree with OWR Theorems 1-3 for n<=40, d<=30
  For k >= 5 = 3r+2 the ANS96/DV21 LB*_1 formula equals Prop 4.1 (generic) and the
  homogeneous values in the proof of Thm 4.2 (other cases), n<=30, k<=30.
   n=3 m=3  k=2..6: Prop4.1 [7, 13, 24, 42, 66]   LB*_1 [6, 12, 24, 42, 66]
   n=4 m=2  k=2..6: Prop4.1 [7, 17, 33, 56, 88]   LB*_1 [8, 16, 32, 56, 88]
   n=4 m=3  k=2..6: Prop4.1 [7, 15, 30, 54, 86]   LB*_1 [6, 14, 30, 54, 86]
   n=4 m=4  k=2..6: Prop4.1 [7, 14, 30, 54, 86]   LB*_1 [6, 14, 30, 54, 86]
   n=5 m=5  k=2..6: Prop4.1 [7, 16, 36, 66, 106]   LB*_1 [6, 16, 36, 66, 106]
   n=6 m=3  k=2..6: Prop4.1 [7, 19, 42, 78, 126]   LB*_1 [6, 18, 42, 78, 126]
==============================================================================
TOTAL mismatches: 0
elapsed 45.0s
