Collisional age after uniform dynamical depletion ($t_{\mathrm{inferred}}=fT+(t-T)$)

If a collision operator is homogeneous of degree two in its bin masses, reducing every mass by $f$ slows the subsequent evolution by $f$. If $m(t)$ is the undepleted trajectory and depletion occurs at $T$, the post-depletion trajectory is $m_d(t)=m(T+(t-T)/f)/f$. Compared with a collision-only model starting with normalization $m(0)/f$, the same observed distribution has inferred age $fT+(t-T)$. The distribution alone cannot distinguish the depletion factor from unknown initial normalization and age.