here is contour-plot version because why not

Clockwise - (1) active (truncated) states, (2) log-scaled probability density of active states, (3) how many states are kept in the truncated space, and (4) truncation error over time.

The idea to dynamically prune the state space based on intensities is not new, but we show that quantile‐based pruning is a better approach as it adapts to the distribution’s shape and ensuring tighter control over error with fewer wasted states.

Using a standard SSA to detect a rare second stable basin often requires millions of runs, since that basin appears in only a tiny fraction of trajectories. In contrast, FSP with pruning systematically retains the small probability mass in that basin, making it far easier to identify.

Our method prunes low‐probability states at each step by applying a quantile cutoff (e.g., bottom 5%) and renormalizing the remainder. This strategy focuses computational effort on the most significant regions, preventing explosive state‐space growth while preserving accuracy.

Classical FSP solves the Chemical Master Equation by projecting the infinite state space onto a chosen subset. If truncation error is high, it expands that subset. Each iteration yields a rigorous approximate solution without enumerating all possible states.