Definition: New fixed-input invariant jet

For a fixed free scalar ${\varphi }_0$, let ${{\mathcal{J}}_{g,{\sigma }_{\epsilon }}}^{\mathrm{D}}({\varphi }_0)$ consist of smooth formal families

for which the coefficients through ${\kappa }^2$ of $e_{\mathrm{D}}=0$ and $E_{\varphi }=0$ vanish. Positive-order scalar coefficients have the inherited zero initial data. Metric Cauchy data are unrestricted.

This is a jet of $S_{\mathrm{D}}$, not of the gauge-fixed action. In particular, ${\gamma }_0$ is not required to vanish.