  To construct asymptotically-Euclidean Einstein's initial data sets, we
introduce the localized seed-to-solution method, which projects from
approximate to exact solutions of the Einstein constraints. The method enables
us to glue together initial data sets in multiple asymptotically-conical
regions, and in particular construct data sets that exhibit the gravity
shielding phenomenon, specifically that are localized in a cone and exactly
Euclidean outside of it. We achieve optimal shielding in the sense that the
metric and extrinsic curvature { are controlled at a super-harmonic rate,
regardless of how slowly they decay (even} beyond the standard ADM formalism),
and the gluing domain can be a collection of arbitrarily narrow nested cones.
We also uncover several notions of independent interest: silhouette functions,
localized ADM modulator, and relative energy-momentum vector. An axisymmetric
example is provided numerically.
