5.7 Doeblin-Type Upper Bound for Information Field Cumulants

Based on (Graph-Theoretic Definition of Information Field Cumulants), this article constructs a **Doeblin-type coupling** on the graph , jointly exploiting Birkhoff mixing () and hard-direction Lyapunov contraction (), to rigorously prove the exponential decay upper bound for the k-th order information field cumulant : where , and is the maximal separation distance of the nodes in the hard direction . Core numerical anchor: — mixing is 156 times faster than contraction; this is the fundamental mechanism by which many-body correlations are "washed out" in the steady state.