  We construct an $\mathcal{N}=2$ supersymmetric gauged quantum mechanics, by
starting from the 3d Chern-Simons-matter theory holographically dual to massive
Type IIA string theory on AdS$_4 \times S^6$, and Kaluza-Klein reducing on
$S^2$ with a background that is dual to the asymptotics of static dyonic BPS
black holes in AdS$_4$. The background involves a choice of gauge fluxes, that
we fix via a saddle-point analysis of the 3d topologically twisted index at
large $N$. The ground-state degeneracy of the effective quantum mechanics
reproduces the entropy of BPS black holes, and we expect its low-lying spectrum
to contain information about near-extremal horizons. Interestingly, the model
has a large number of statistically-distributed couplings, reminiscent of SYK
models.
