= Solution
Differentiating $\mathbf g=\epsilon_0\mathbf E\times\mathbf B$, substituting <Maxwell equations>, and using the stated <vector> identity gives the <Maxwell stress tensor> conservation law
$$
\partial_tg_j
=\partial_i\left[\epsilon_0\left(E_iE_j-\frac12E^2\delta_{ij}\right)
+\frac1{\mu_0}\left(B_iB_j-\frac12B^2\delta_{ij}\right)\right]
-(\rho\mathbf E+\mathbf J\times\mathbf B)_j.
$$
Moving the divergence to the left identifies
$$
\widetilde a=-\epsilon_0,
\quad \widetilde b=\frac{\epsilon_0}{2},
\quad \widetilde c=-\frac1{\mu_0},
\quad \widetilde d=\frac1{2\mu_0}.
$$
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