P(survive, t) ~ 1/t at criticality; size distribution P(s) ~ s^(−3/2)
Surviving: 0 | Mean size: 0 | Median lifetime: 0
Galton-Watson branching process: each individual independently produces a random number of offspring.
At criticality (mean m = 1), the process is certain to go extinct (Yaglom 1947) but survives for a long time.
Survival probability P(Z_t > 0) ~ 2/(σ²t) for large t. Conditioned on survival, population size ~ t.
Size distribution at extinction P(total=s) ~ s^(-3/2) — the same exponent as neural avalanches.