5.6 Graph-Theoretic Definition of Information Field Cumulants

This article provides a graph-theoretic precise definition of information field cumulants, filling G1 in the proof framework of "information field cumulant factorization." The definition has two levels: the base Clifford graph () and the parameter-space fine-grained graph (). The two levels share the same algebraic structure, differing only in node count. Core result: the upper bound of the k-th order cumulant is jointly controlled by the Birkhoff spectral gap and the hard-direction Lyapunov exponent .