= Halo abundance mass-budget bound
{title2=$\int M\,n_h(M)\,dM\leq\bar\rho_{m,0}$}
A population of distinct, nonoverlapping <dark-matter halos> cannot contain more total mass per <comoving volume> than the cosmic mean matter density. A narrow mass population therefore obeys $n_cM_h\leq\bar\rho_{m,0}$. Do not sum subhalo masses and their inclusive host masses in the same bound, because that double-counts material. This check can reveal incompatible inferred absorption incidence, object size and halo-mass assumptions.
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