= Mass-spectrum transport under quadratic accretion
{title2=$F(M,t)=F_0(M/(1+\lambda tM))/(1+\lambda tM)^2$}
If stars are neither created nor lost and all follow <quadratic accretion in a central Keplerian potential>, conservation of number gives $F(M,t)dM=F_0(M_0)dM_0$. Inverting the trajectory gives $M_0=M/(1+\lambda tM)$ and its <Jacobian determinant> is $(1+\lambda tM)^{-2}$. This proves the displayed mass-density-in-mass-space transformation. In a broad high-mass range with $\lambda tM\gg1$, whose inverse images remain in a narrow interval where $F_0$ varies little, the <power law> is $F\propto M^{-2}$. A strictly monochromatic initial population remains monochromatic. Finite initial support imposes a finite upper cutoff before the earliest formal blow-up, so the power law is an intermediate asymptotic subject to the accretion model's limits.
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