Fold Bifurcation and Friction Divergence in Capacity-Constrained Compounding Systems

We propose a minimal dynamical model for capacity-constrained compounding in which the fast dynamics take the saddle-node normal form. Given this model, we verify that the standard nondegeneracy and transversality conditions hold and derive two consequences: a fold bifurcation at the capacity boundary, and divergence of coordination cost (friction) along the attracting equilibrium branch with scaling F ~ (Q - V)^{-1/2}. We classify the fold as a jump point in the Krupa-Szmolyan taxonomy: the desingularized slow flow is nonzero at the fold, the 1/x singularity resolves under the standard (1,2,2)-weighted blow-up, and the friction coupling creates a barrier that prevents endogenous approach to the fold. Collapse requires exogenous load growth that overwhelms this friction feedback. The model generates four testable predictions about fold-consistent dynamics (critical slowing down, variance scaling, delayed recovery, and threshold structure). We specify an empirical protocol for testing the scaling exponent via linearized regression, with a three-model comparison design that distinguishes fold scaling from generic power-law divergence.