= Press-Schechter abundance growth at fixed mass
{c}
{title2=$\partial_t\ln n\big|_M=(\nu^2-1)\dot D/D$}
For a fixed narrow mass bin with time-independent smoothing slope, the <Press-Schechter halo mass function> has time dependence $n\propto\nu e^{-\nu^2/2}$, with <halo peak height> $\nu\propto D^{-1}$. Differentiating gives the displayed rate. It is positive only for $\nu>1$; the bin can lose objects to higher masses later. Cumulative counts require integrating the differential abundance, and a moving mass boundary adds a selection term.
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