Topological Void Mapping in Actuarial Science: Pricing Systemic Cyber-Contagion via Dirichlet Boundary Conditions and Fibrated Tensor Spaces

Abstract

Classical cyber-actuarial models rely on historical Poisson distributions and Gaussian covariance matrices to predict loss frequency and severity. However, these stochastic models structurally fail during systemic supply-chain exploits, where network correlations artificially converge to unity and probabilistic diversification collapses. This paper introduces the Chrysene Formalism to actuarial science, transitioning systemic risk underwriting from stochastic behavioral prediction to deterministic spatial geometry. By mapping digital supply chains into a discrete, fibrated manifold designated as the Chrysene Tensor Space, we evaluate structural fragility through the isomorphic mapping of negative space. Utilizing algebraic homology, we identify systemic vulnerabilities as deterministically computable ``Ghost Pockets'' lacking internal Dirichlet boundary conditions. We mathematically formulate cyber-breaches as Topological Scission events, proving that contagion propagates as an anisotropic diffusion wave governed by the discrete graph Laplacian. This framework allows reinsurers to calculate the absolute Volumetric Collapse of a network, transitioning insurance pricing from Expected Value estimations to strictly bounded spatial integrals, thereby monetizing absolute orthogonal portfolio decoupling.