theorem network_persistence_buffer {J_low J_high ρ c cost : ℝ}
(hJl : 1 < J_low) (hJlh : J_low < J_high)
(hρ0 : 0 < ρ) (hρ1 : ρ < 1) (hc : 0 < c)
(hcost : cost ≤ valueFunction J_low ρ c) :
cost < valueFunction J_high ρ c := by
have hV := valueFunction_increasing hJl hJlh hρ0 hρ1 hc
linarithPaper 3c, Section 3: First-Order Regime Shift