= Elliptic existence of a Witten spinor
On complete smooth asymptotically flat <spin> initial data without inner boundary, satisfying the Einstein constraints and the <dominant energy condition>, the <Witten spinor equation> admits a spinor approaching each prescribed asymptotic constant, under the standard weighted decay assumptions. The integrated <Witten-Nester identity> gives a coercive estimate and excludes a decaying homogeneous kernel. Weighted elliptic solvability then supplies the desired correction to a spinor extended from infinity. Positivity of the boundary integral is a conditional identity until this analytic existence step is supplied; see https://users.math.msu.edu/users/parker/witten.pdf[the rigorous analytic proof].
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