Constraint-Bounded Transport Exhibits a Bounded Optimal Coupling Regime: An Invariance Test of ΔΦ-Based Dynamics

This work tests whether a fixed optimal coupling constant (p* ≈ 0.106) universally governs transport efficiency in systems described by ΔΦ = ρ × v.A constraint-bounded transport model was evaluated across multiple graph topologies, system sizes, noise levels, and update rules. The results show that p* is not invariant and varies significantly across implementations.However, all tested systems exhibit a consistent structural pattern: transport efficiency peaks within a bounded intermediate coupling regime. Both under-coupling and over-coupling degrade performance.The central finding is that constraint-bounded transport systems exhibit a robust optimal coupling regime rather than a fixed optimal value. This reframes the hypothesis as a constraint-defined phase structure.