interior points whose R-column sums to 0 (then (0,1) = (a_p,1) - sum_rho R[rho,p] (e_rho,1) + (sum_rho R[rho,p] - 0)(...)): [(2, 2, 2)] ; column sums: [-2, -1, 0]
d=2: classes without integer point according to HiGHS (candidates): 18; 1s
   exact: certified without integral point (a coordinate range without integer): 18; single points: 18; with an integer t in the exact range of sum(x): 6; 2s
d=3: classes without integer point according to HiGHS (candidates): 30; 147s
   exact: certified without integral point (a coordinate range without integer): 30; single points: 6; with an integer t in the exact range of sum(x): 30; 149s
   example: x = (0, 0, 0, 1, 1, 0, 1, 1, 0, 1)/2; coordinate h(1, 4, 1) ranges exactly over [1/2, 1/2]; sum of all coordinates ranges exactly over [13, 13]; b* entries in [-1, 0, 1]
   example: x = (0, 1, 1, 1, 0, 0, 0, 0, 1, 1)/2; coordinate h(1, 2, 3) ranges exactly over [1/2, 1/2]; sum of all coordinates ranges exactly over [13, 13]; b* entries in [-1, 0, 1]
   example: x = (1, 0, 0, 0, 1, 0, 1, 0, 1, 1)/2; coordinate h(1, 1, 4) ranges exactly over [1/2, 1/2]; sum of all coordinates ranges exactly over [13, 13]; b* entries in [-1, 0, 1]
   example: x = (1, 0, 1, 1, 1, 0, 0, 1, 0, 0)/2; coordinate h(1, 1, 4) ranges exactly over [1/2, 1/2]; sum of all coordinates ranges exactly over [13, 13]; b* entries in [-1, 0, 1]
the point phi of the claim: sum of the coordinates of h~* = 25/2
