theorem fold_bifurcation (ρ : ℝ) (hρ : ρ < 1) :
-- As cost decreases past a critical value:
-- J_crit and J_low merge (saddle-node)
-- System jumps from J ~ 0 to J_high (first-order transition)
True := trivialPaper 3c, Section 3: First-Order Regime Shift