Corrected root current

Two divergence operators are kept distinct. $D_{\mathrm{div}}T={\partial }_{\mu }{T}^{\mu \nu }$ and $D_{\mathrm{gf}}r={\partial }_{\mu }(\mathcal{P}r{)}^{\mu \nu }=D_{\mathrm{div}}\mathcal{P}r$, with formal adjoints ${D^{\star }}_{\mathrm{div}}v=-{\partial }_{(\mu }{v}_{\nu )}$ and ${D^{\star }}_{\mathrm{gf}}=\mathcal{P}{D^{\star }}_{\mathrm{div}}$. From the displayed linearized Einstein operator,

For $a_{\mathrm{root}}=-E^A\mathcal{P}\alpha$,

The superseded vector $E^A(D_{\mathrm{div}}\mathcal{P}\alpha )$ is wrong for traceful $\alpha$. Every r7 value computed for that vector is withdrawn. Since $D_{\mathrm{div}}A=0$, one has $D_{\mathrm{div}}H=0$.

For symmetric $H$, the root current of the reduction is

and $s_0{F}_t=⟨C,\xi ⟩$ for $\xi$ supported in the plateau. On $U$, equivalently, $s_0{F}_t=-2⟨w,D_{\mathrm{gf}}({\mathcal{L}}_{\xi }h)⟩$.