  We revisit the D0 bound state problems, of the M/IIA duality, with the
Orientifolds. The cases of O4 and O8 have been studied recently, from the
perspective of five-dimensional theories, while the case of O0 has been much
neglected. The computation we perform for D0-O0 states boils down to the Witten
indices for $\mathcal N=16$ $O(m)$ and $Sp(n)$ quantum mechanics, where we
adapt and extend previous analysis by the authors. The twisted partition
function $\Omega$, obtained via localization, proves to be rational, and we
establish a precise relation between $\Omega$ and the integral Witten index
$\mathcal I$, by identifying continuum contributions sector by sector. The
resulting Witten index shows surprisingly large numbers of threshold bound
states but in a manner consistent with M-theory. We close with an exploration
on how the ubiquitous rational invariants of the wall-crossing physics would
generalize to theories with Orientifolds.
