ADM boundary term of the Nester two-form ($(8\pi G{)}^{-1}\lim \int b^i{s}_{i}dS=E{K}_{\infty }^0-P_i{K}_{\infty }^i$)

For asymptotically constant spinors, the leading intrinsic spin connection term gives half the ADM metric integrand times $K_{\infty }^0$. The Sen spinor connection correction gives $-(k_{ij}-k{h}_{ij})K_{\infty }^j$. The constant-spinor derivative term integrates to zero by antisymmetry of the gamma matrices, and the remaining quadratic terms vanish under the standard decay. This identifies the Nester two-form flux with the ADM energy-momentum contraction, including momentum rather than just energy.