  The uncharged AdS$_4$ soliton has been recently shown to be continuously
connected to a magnetic, supersymmetric AdS$_4$ soliton within $\mathcal{N}=8$
gauged supergravity. By constructing the asymptotic superalgebra, we establish
a positive energy theorem for the magnetic AdS$_4$ solitons admitting
well-defined asymptotic Killing spinors, antiperiodic on a contractible $S^1$.
We show that there exists only one discrete solution endowed with these
boundary conditions satisfying the bound, the latter being saturated by the
null energy supersymmetric configuration. Despite having negative energy, the
uncharged AdS$_4$ soliton does not contradict the positive energy theorem, as
it does not admit well-defined asymptotic Killing spinors.
