Continuity of finite-cluster mass at the onset of Flory gelation

We prove continuity of the finite-cluster mass at the gelation time for every weak Flory solution with a continuous symmetric kernel comparable to $x^\alpha y+xy^\alpha$, where $0<\alpha<1$, and a finite initial measure of unit first moment. No higher initial moment is required. A hypothetical jump forces a positive amount of mass into a finite band at sizes of order $(T_g-t)^{-1/\alpha}$. A time-dependent exponential test shows that a fixed positive fraction of this band mass remains in finite clusters at $T_g$, contradicting the vanishing tails of the finite mass measure at that time.