  Building on the recent discovery of the first candidate black hole operator
in $\mathcal{N}=4$ super-Yang-Mills, we explore the near-supersymmetric aspects
of the theory that capture lightly excited, highly stringy black holes. We
extend the superspace formalism describing the classically supersymmetric
(1/16-BPS) sector of $\mathcal{N}=4$ super-Yang-Mills and compute a large
number of one-loop anomalous dimensions. Despite being in the highly stringy
regime, we find hints of a gap in the spectrum, similar to that found by a
gravitational path integral. We also determine the actual expression of the
first candidate black hole operator at weak gauge coupling, going beyond the
cohomological construction.
