This work establishes a governing principle for nonlinear transport systems: optimal coupling is not a fixed parameter, but a constraint-dependent attractor. Building on the ΔΦ Coupling Constraint Law, this study demonstrates that coherent transport emerges only when structural constraints are intact, collapses when those constraints are degraded, and reappears upon restoration.Using the ΔΦ Biological State Transition Engine v5.0, controlled deformation experiments reveal that optimal coupling (p*) consistently converges within narrow bands under valid conditions, disperses under constraint violation, and reconverges when the system’s internal structure is reinstated. This reversible behavior confirms that transport efficiency is not driven by increased connectivity, but by the preservation of constraint integrity.The results unify coupling optimization, regime transitions, and transport coherence into a single framework governed by ΔΦ = ρ × v, where active density and delivery flow remain tightly coupled across conditions. The principle introduces a falsifiable criterion for identifying when systems will sustain coherent transport and when they will fail, with implications spanning intracellular transport, distributed computation, swarm systems, and network design.Rather than maximizing interaction, efficient systems operate at the lowest coupling that preserves continuity—and only when the underlying constraints allow that attractor to exist.
Thomas S. Mitchell (Sat,) studied this question.