Universal Coupling Collapse Bound

We study coupled discrete-time systems of Kronecker-sum type M = I_m ⊗ A + C ⊗ I_n where A is the internal dynamics and C is the coupling operator. We introduce the dimensionless Coupling Collapse Index Icc(A,C) = ||C||₂ R∞(A) and prove that the condition Icc(A,C) < 1 yields a resolvent bound, a Kreiss constant bound, and a transient amplification bound. The result is sharp for normal A, conservative for non-normal A, and extends naturally to heterogeneous agent populations.