PhronesisThe displacement framework's first eight conditions describe ground state, cost, return gradients, path dependence, irreversibility, mutual displacement, accumulation, and extraction. We identify DC9: threshold dynamics. Below critical displacement ξ_c, perturbations are sub-critical—return gradient dominates and the system recovers to ground state. Above ξ_c, perturbations are super-critical—displacement becomes autocatalytic, driving the system to maximum displacement regardless of subsequent input.
We call this projectile dynamism: once threshold is crossed, the system is launched on a committed trajectory. The canonical case is the action potential: the neuron depolarizes to -55 mV, voltage-gated Na+ channels cascade open, and the full spike fires regardless of subsequent input. The all-or-nothing law is DC9 in its clearest form. We generalize to epidemic thresholds (R0=1), climate tipping points, Granovetter social revolution thresholds, psychological breakdown/breakthrough, and addiction allostasis.
DC9 predicts post-threshold refractory undershoot—the system overshoots ground state after maximum displacement, connecting to the below-baseline condition.