= Efficiency upper bound from Eddington-limited growth
{title2=$\eta\leq\Delta t/[\Delta t+t_E\log(M_f/M_i)]$}
For fixed efficiency, growth from $M_i$ to $M_f$ within $\Delta t$ at no more than the <Eddington luminosity> requires $[\eta/(1-\eta)]t_E\log(M_f/M_i)\leq\Delta t$. Solving gives an upper bound, because greater radiative efficiency reduces retained <mass> growth at a fixed <luminosity>. A duty cycle below unity tightens the requirement; mergers and super-Eddington episodes invalidate its stated premises.
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