== copy of the claim's check_abb3d.py on MY certificate mycert_ABB_3D.json
terms: 437; monomials after expansion: 15245; Qden = 589824; max |Z| = 2602694
(a) all congruence-class sums vanish: True
(b) max over all 2^27 patterns of 9*Qden*(Psi0 + Q) = 31850496;  54*Qden = 31850496;  valid = True
    patterns with equality: 39;  largest value below the bound = 54*Qden - 848466
(L) appearances of ABB in the 3x3x3 grid with A on a coordinate plane: 162; size 27; concentration 162/27
(E) the patterns with equality are exactly the 39 hyperplane windows: True
(E) unique continuation of hyperplane windows along the three axes: True
CERTIFICATE VALID: Psi0 + Q <= 6 on all patterns; hence C_3(ABB) <= 6, and (L) gives equality.
exit status 0

== copy of the claim's check_abb3d.py on the claim's cert_ABB_3D.json
terms: 160; monomials after expansion: 4941; Qden = 1451520; max |Z| = 5362624
(a) all congruence-class sums vanish: True
(b) max over all 2^27 patterns of 9*Qden*(Psi0 + Q) = 78382080;  54*Qden = 78382080;  valid = True
    patterns with equality: 39;  largest value below the bound = 54*Qden - 155376
(L) appearances of ABB in the 3x3x3 grid with A on a coordinate plane: 162; size 27; concentration 162/27
(E) the patterns with equality are exactly the 39 hyperplane windows: True
(E) unique continuation of hyperplane windows along the three axes: True
CERTIFICATE VALID: Psi0 + Q <= 6 on all patterns; hence C_3(ABB) <= 6, and (L) gives equality.
exit status 0
