  We prove a positive mass theorem for spin initial data sets $(M,g,k)$ that
contain an asymptotically flat end and a shield of dominant energy (a subset of
$M$ on which the dominant energy scalar $\mu-|J|$ has a positive lower bound).
In a similar vein, we show that for an asymptotically flat end $\mathcal{E}$
that violates the positive mass theorem (i.e. $\mathrm{E} < |\mathrm{P}|$),
there exists a constant $R>0$, depending only on $\mathcal{E}$, such that any
initial data set containing $\mathcal{E}$ must violate the hypotheses of
Witten's proof of the positive mass theorem in an $R$-neighborhood of
$\mathcal{E}$. This implies the positive mass theorem for spin initial data
sets with arbitrary ends, and we also prove a rigidity statement. Our proofs
are based on a modification of Witten's approach to the positive mass theorem
involving an additional independent timelike direction in the spinor bundle.
