We revamp the constructive enumeration of 1/16-BPS states in the maximally
supersymmetric Yang-Mills in four dimensions, and search for ones that are not
of multi-graviton form. A handful of such states are found for gauge group
SU(2) at relatively high energies, resolving a decade-old enigma. Along the
way, we clarify various subtleties in the literature, and prove a
non-renormalization theorem about the exactness of the cohomological
enumeration in perturbation theory. We point out a giant-graviton-like feature
in our results, and envision that a deep analysis of our data will elucidate
the fundamental properties of black hole microstates.Comment: 13 pages, 2 figures, 5 tables; v2, v3: minor revisions, references
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