La Profilée - Coupling Theorem of Persistence: Structural Extension of IR ≤ 1 to Coupled Systems

La Profilée’s persistence condition IR = R / (F · I · C) ≤ 1 was derived for a single system. The present paper extends the framework to structurally coupled systems. When two persistent systems A and B are structurally coupled, coupling operates through two structural channels: numerator-effective transformations (load transfer α and transformation shielding σ, both acting on R_eff) and denominator-effective transformations (integration distribution β, acting on IK_eff). These channels are structurally distinct, asymmetrically conditioned, and state-dependent — their relative magnitudes determine whether coupling stabilizes or destabilizes each system. The paper derives the structural consequences. Coupling shifts the effective values of R and IK for each system: R_eff and IK_eff are no longer determined by the system’s own structure alone but by its structure together with the coupling relation. The persistence condition for each system must therefore be evaluated at these effective values. A system can satisfy IR ≤ 1 in isolation and violate it under coupling, or violate IR ≤ 1 in isolation and satisfy it under coupling. The paper establishes that coupled systems constitute a system of higher order — System AB — with its own persistence condition IR_AB. IR_AB is not the average or sum of IR_A and IR_B but a structural function of R_AB and IK_AB, which themselves depend on the coupling relation. A critical consequence follows: a system can become structurally critical or structurally stable without any change in its own internal structure — through coupling alone. Coupling does not create stability. It shifts the structural conditions under which stability holds.