Three successor objects

Before posing a sourced problem, specify an action and source normalization, the coefficient equation space, its gauge group, support classes, and initial or boundary conditions. An evaluation set is not a quotient unless an action preserving that set and the resulting equivalence relation have been supplied.

For definiteness, one possible future gauge specification is the initial-surface-fixing subgroup

It is contained in ${\mathcal{G}}_{\mathrm{R}}$, and its fields vanish on a neighborhood of the initial surface. A formal second-order prescription could take both coefficient descriptors in this group. This is not the C1 residual-wave group.

For a sourced successor, allow smooth metric coefficients unless a separate asymptotic class is proved appropriate. Do not impose compact metric data merely because the scalar data are compact. Scalar coefficients may be required to be spacelike compact. Invariant initial metric data must satisfy their sourced constraints; arbitrary zero metric data are not automatically admissible.