Spectral Asymptotics of Latency-Weighted Relativistic Hypergraphs: Deriving Cheeger-Type Stability Bounds for Anisotropic Galactic Trade Multiplexes

Mathematical Applications of Science Fiction We investigate the spectral properties of a class of latency-weighted hypergraphs embedded in a ((3 + 1))-dimensional Lorentzian manifold, serving as a model for anisotropic galactic trade multiplexes subject to relativistic causality constraints. By defining a Lorentz-covariant adjacency tensor and a subsequent proper-time weighted Laplacian ( L_\tau ), we analyze the asymptotic behavior of the spectral density as the network size ( N \to \infty ). We derive a rigorous Cheeger-type inequality that bounds the second eigenvalue ( \lambda_2 ) (the algebraic connectivity) in terms of the isoperimetric constant of the causal diamond foliation. Furthermore, we demonstrate that for anisotropic trade topologies driven by Kerr-metric geodesics, the spectral gap exhibits a stability phase transition governed by the frame-dragging angular momentum parameter ( a ). These results provide a theoretical framework for optimizing synchronization protocols in superluminal-latency constrained communication networks.