5.8 Uniform Boundedness of Information Field Cumulants

In the established exponential decay upper bound for information field cumulants, the combinatorial factor explicitly contains . As (continuum limit), superficially helps suppress cumulants, but the real challenge is whether the spectral gap remains finite and positive in the limit — if , the exponential decay will degenerate, potentially offsetting the gain from the combinatorial factor. This article provides a twofold proof: (1) via the **fibration structure** of the information field graph over the Clifford graph , we rigorously prove that the mixing rate (spectral gap) is a fibration invariant — is the same at all scales; (2) under Assumption A.1, we directly establish a finite upper bound for the continuous cumulant density that is independent of . The two together provide a complete fill.