  By using the approach introduced in arXiv:2107.09677 we construct non-BPS
solutions of 6D $(1,0)$ supergravity coupled to two tensor multiplets as a
perturbation of AdS$_3\times S^3$. These solutions are both regular and
asymptotically AdS$_3\times S^3$, so according to the standard holographic
framework they must have a dual CFT interpretation as non-supersymmetric heavy
operators of the D1-D5 CFT. We provide quantitative evidence that such heavy
CFT operators are bound states of a large number of light BPS operators that
are mutually non-BPS.
