five-point positive control G5*D5 = [[1, -1]]
hard-particle invariants: [2, 3, 5, 7, 11, -28]
s_iP: [-10, -20, 18, 12]
G6 = [[12, -18, 0, 0, -18, -20], [0, 0, 12, 20, 18, 20]]
R6 = [[72, 126, 0, 0, -72, -200], [0, 0, 72, 260, -162, -300], [48, 162, -36, -200, 0, 0]]
rank([G6;R6]) = 5
right kernel = [10/13, 20/39, -10/7, 6/7, -10/9, 1]
diagonal Heaviside defect G6*diag(d)*[1,h23,h24,h34] = [[0, 20, 0, 120/13], [0, -20, -120/7, 0]]
Varchenko first-row ideal Groebner basis = [1]
linearized determinant = -64*(z - 1)*(z + 1)*(189*z**2 - 608*z + 189)
Segre defect = -64*(z + 1)**2*(7551*z**4 + 29650*z**3 - 70178*z**2 + 29650*z + 7551)
z=-1 linear solution (xy,x,y) = {(-1, 9/5, -9/5)}
sign-twist Groebner certificates = {('plain', 'plain'): [1], ('plain', 'sign'): [1], ('sign', 'plain'): [1], ('sign', 'sign'): [1]}
six-point reconstruction factors = [-10, -20, 18, 12, -26, 14, 12]
all exact six-point obstruction checks passed
