Radioactivity

Keep two independent ledgers for a decay or decay chain. An alpha emission lowers the mass number by $4$ and the proton number by $2$; a beta${}^{-}$ emission leaves the mass number unchanged and raises the proton number by $1$ (a neutron turns into a proton).

Trigger: a decay described by counts of alpha and beta particles, or by a net change in mass number or proton number.

Instances:
(i) net proton change $\Delta Z=-2n_{\alpha }+n_{\beta }$, net mass change $\Delta A=-4n_{\alpha }$.
(ii) since only alpha changes the mass number, read $n_{\alpha }=\Delta A/4$ straight off the mass drop, decoupled from the betas, then recover $n_{\beta }$ from $\Delta Z$.
(iii) with a single alpha in the chain, the mass number can only ever be the start value or that value minus $4$, and beta steps only raise $Z$, so any nuclide off those two mass numbers (or below the starting $Z$ while the mass is unchanged) is unreachable.