     Ae  entry sums n=1..8: 1, 5/2, 4, 6, 9, 25/2, 16, 20
ok   Ae: Kasteleyn signing; |det| = 2^(n(n+1)/2); +-1 gauge to K_n found and verified; sum predicted from K_n^-1 and the gauge = direct sum
ok   Ae: entry sums as stated in the note (n <= 8)
     Ae differs from the formula for n in [4, 5, 6, 7, 8]
     Ao  entry sums n=1..8: 1, 5/2, 4, 6, 9, 25/2, 16, 20
ok   Ao: Kasteleyn signing; |det| = 2^(n(n+1)/2); +-1 gauge to K_n found and verified; sum predicted from K_n^-1 and the gauge = direct sum
ok   Ao: entry sums as stated in the note (n <= 8)
     Ao differs from the formula for n in [4, 5, 6, 7, 8]
     KWl entry sums n=1..8: 1, 5/2, 11/2, 8, 13, 31/2, 45/2, 23
ok   KWl: Kasteleyn signing; |det| = 2^(n(n+1)/2); +-1 gauge to K_n found and verified; sum predicted from K_n^-1 and the gauge = direct sum
ok   KWl: entry sums as stated in the note (n <= 8)
     KWl differs from the formula for n in [3, 4, 5, 6, 7, 8]
     KWu entry sums n=1..8: 1, 5/2, 11/2, 8, 13, 31/2, 45/2, 23
ok   KWu: Kasteleyn signing; |det| = 2^(n(n+1)/2); +-1 gauge to K_n found and verified; sum predicted from K_n^-1 and the gauge = direct sum
ok   KWu: entry sums as stated in the note (n <= 8)
     KWu differs from the formula for n in [3, 4, 5, 6, 7, 8]
     HE  entry sums n=1..8: 1, 5/2, 4, 9/2, 2, -15/2, -32, -175/2
ok   HE: Kasteleyn signing; |det| = 2^(n(n+1)/2); +-1 gauge to K_n found and verified; sum predicted from K_n^-1 and the gauge = direct sum
ok   HE: entry sum = the formula for every n <= 8
ok   Remark 6.1: exactly one -1 at every black square with four neighbours for the Problem 12 signs
ok   Remark 6.1: this fails at every such square for the alternate-columns signs
ok   Remark 6.1: for Kasteleyn-Wilson it fails exactly in the row y = 1/2 (lower-row reading) / y = -1/2 (upper)
ok   HE (Helfgott's vertical-edge-count signing) = Problem 12 signs edge for edge: colouring 'black iff x+y odd' for even n, the other colouring for odd n (n <= 8)
TOTAL: 0 failed  (1.5 s)
