Algebraic Connectivity of Chrono-Anisotropic Multiplexes: Establishing the Lower Bound of Network Resilience in Relativistic Trade Hyper-structures via the Laplacian Spectrum of Non-Hermitian Adjacency Matrices

Mathematical Applications of Science Fiction We present a rigorous operator-theoretic framework for analyzing the structural resilience of relativistic trade networks modeled as chrono-anisotropic multiplexes. Unlike classical graph theory, where edge weights are static scalars, we consider a Lorentzian manifold embedding in which edge existence is governed by light-cone causality and weights transform according to the reference frame of each node. This leads to the definition of a non-Hermitian Supra-Laplacian operator. We investigate the algebraic connectivity of such systems, defined not by the second eigenvalue of a symmetric matrix, but by the minimal real part of the spectrum of a non-normal Laplacian in the complex plane. We derive a fundamental lower bound for this connectivity, termed the Faustus Resilience Criterion, using a generalized Cheeger inequality for Finsler geometries and the field of values of the adjacency operator. Finally, we prove that as the relative velocity between network layers approaches the speed of light, the spectral gap collapses asymptotically with the square of the Lorentz factor, implying a catastrophic loss of coherence in hyper-relativistic trade structures.