Metric Source Completions and Integrability in Celestial Gravity

We evaluate local metric-source responses of celestial Einstein scattering in Weyl–Beltrami variables. Compact physical graviton packets retain the momentum-conservation distribution and its normal derivatives. For disjoint smooth Beltrami profiles, the complete reference same-chirality Ward response agrees with the differentiated quasiconformal source functional through quadratic order. Subtracting the symmetrized product response isolates a nonzero nonlinear coordinate contribution, detected by a linear normal packet independently of the quadratic normal coefficient. An analytic normal-profile subclass supports angular continuation on compact unpinched regions and permits evaluation of the MHV energy corner and relative Banerjee–Pasterski endpoint residue. For opposite helicities, consecutive soft theorems determine the energy and spin contributions to the full momentum distribution. A real Kawai–Lewellen–Tye channel gives its nonzero normal coefficient and the mixed Mellin divisor of a gravitational contact. We formulate the additional global Ward, contact and continuation conditions for a mixed metric Hessian. Reference scattering data, source transport and vacuum completion enter separately in this construction. In the scalar sector, an area-normalized relative determinant fixes the anomaly functional, and fixed-area harmonic combinations extract its Euler coefficient from local curvature terms of bounded derivative order. These calculations provide physical response data and local continuation domains for integrable celestial metric-source completions.