A Structural Law for Instability in Finite-Capacity Transport Systems

This paper proves that four structural conditions: conservation form, distributed loading, finite saturating export, and monotone forcing, are sufficient to place a transport system generically in a single instability class, independently of its physical medium or biological implementation. From these premises alone, a necessary feasibility coordinate σ = ΣJ_in / J_max is derived, and it is proved that any system satisfying the conditions must lose its attracting equilibrium branch at a finite parameter value through a codimension-one saddle-node fold bifurcation. The reserve margin R = J_max − ΣJ_in enters the fold normal form as the leading-order unfolding parameter, establishing a coordinate identity between the feasibility boundary and the fold boundary. Two universal dynamical signatures follow: recovery time scaling as τ ~ R^(−1/2) and slow-passage delay scaling as ΔT ~ ε^(−1/3). A necessity proposition is proved: any framework reproducing the joint prediction set must be locally equivalent, near the instability boundary, to the transport-reserve normal form. Spreading depolarisation in excitable tissue is identified as the primary physiological instantiation of the class. This is the fourth and final paper of the SES theoretical programme.