Remark: Explicit matched functional; certificates

Certificate A, in the formal reading, is the single coordinate $C[N=4,b=\{(),0222\},\gamma =()]=1$. It gives

with all other components zero, and

The Gate V Euler derivative of $I_C$ is computed by an independent sympy total-derivative route (jet_euler.py) and equals $E_C$ exactly. Certificates B ($D=4$) and B2 ($D=2$), in the double plateau, are $C[N=4,\{(),0222\},\gamma =0002]$ and $C[\dots ,\gamma =02]$. For example, B gives $E^{00}=-\frac{56}{3}{{\partial }_0}^3{\partial }_2{h}_{02}$, $E^{02}=-\frac{28}{3}{{\partial }_0}^3{\partial }_2(h_{00}+h_{22})$, $E^{22}=-\frac{56}{3}{{\partial }_0}^3{\partial }_2{h}_{02}$, and $I_C=-\frac{28}{3}\int (h_{00}{{\partial }_0}^3{\partial }_2{h}_{02}+{{\partial }_0}^3{\partial }_2{h}_{00}{h}_{02}+h_{02}{{\partial }_0}^3{\partial }_2{h}_{22}+{{\partial }_0}^3{\partial }_2{h}_{02}{h}_{22})$. For a non-self-adjoint unit vector (negative control C) the Euler derivative of $I_C$ differs from $E_C$. All certificates are in helmholtz_certificates.txt.