Remark: The necessary support correction

The Newton position data in (eq:metricdata) generally have tails. They are not compact-Cauchy metric data. Their restrictions to ${\Sigma }_0$ are declared before evolution.

There is no incoming lateral data for the subsequent wave problem on ${\mathcal{D}}_{R,b}$. That statement does not turn the initial Newton prescription into a local source-acquisition operation. In particular, the construction proves no worldsheet boundary condition and no global conical solution.