This paper presents a minimal nonlinear framework for the acute-to-chronic pain transition (Theory and Hypothesis paper). Central claim: therapeutic hysteresis — the intervention intensity required for sustained remission from established chronic pain structurally exceeds the intensity that would have prevented chronification. This is derived from the bifurcation geometry of a two-ODE system (Theorem 1, formally proved). Framework: pain state S = F × E × (1/N) with endogenous flux F_int(S) = kS. Loop gain G = k·α·γ / (β·δ·N₀), bifurcation at Gc = 1 (Jacobian proof). Parameters chosen so G = k (verifiable by inspection). Hill-type extension F_int = kS/(1+sS) produces a subcritical bifurcation, making hysteresis more severe — the linear model is conservative. Ten published findings are consistent with framework predictions. Order-of-magnitude check: observed OR = 1.98 (Carlesso et al. 2019, n=852) is quantitatively more consistent with the multiplicative prediction (2.0) than the additive prediction (1.82). Identifiability quantified: three repeated QST/CPM sessions per patient yields CV(G) ≈ 25% per patient; CV(mean G) ≈ 1.8% for n=200 cohort. Falsifiable at three independent levels: no multiplicative interaction rejects Postulate 1; no composite score advantage rejects the D-RPS; no treatment-prevention asymmetry rejects Theorem 1. Power for P-P5: n ≈ 200 per arm (DeLong method, α=0.05, power=80%). Simulation code: https://doi.org/10.5281/zenodo.19372816 Intended submission: Frontiers in Systems Neuroscience (Hypothesis and Theory, Pain and Nociception section).