We construct infinitely many new \( \frac{1}{16} \) -BPS cohomologies of the 4d maximal super-Yang-Mills theory and interpret them as a black hole wrapped by dual giant graviton hairs. Since the black hole inside a dual giant feels the RR 5-form flux reduced by one unit, its microstate should essentially be an SU(N – 1) cohomology. However, due to the fortuitous nature of the black hole microstates, promoting an SU(N – 1) black hole state to SU(N) generally fails to yield a cohomology. We show at N = 3 that suitable fusion products with the dual giants yield cohomologies. The core black hole size is probed by the minimal size of the dual giant which can wrap it. We also discuss two types of large black hole hairs: large conformal descendants of gravitons and large dual giants. We prove that any SU(N) black hole cohomology admits infinitely many hairs of the first type.
