Most unstable softened disk wavenumber
= Most unstable softened disk wavenumber
{title2=$s_*=e^{-\delta s_*}(1-\delta s_*),\quad s_*<(1+\delta)^{-1}$}
With $s=Q c_sk/\kappa$ and $\delta=\kappa\epsilon/(Q c_s)$, maximize $F(s)=2se^{-\delta s}-s^2$. Its unique positive critical point satisfies the displayed equation. For positive <gravitational softening>, $e^{-\delta s_*}<1$ and $1-\delta s_*>0$, giving the strict bound. Unsoftened gravity has $s_*=1$.