A Finite-Element Analogy for Distributed Computing Resilience: Predictive, Non-Invasive Resiliency Engineering Beyond Chaos Testing

We present a predictive, telemetry-compatible finite-element (FEA) analogy for dis- tributed computing resilience. Traffic is modeled as load vectors, latency/error/saturation as strain components, and capacity & coupling as a stiffness matrix. We derive node and system resilience scores, a von-Mises–style fragility metric, closed-form critical-load predictions, and cascade propagation conditions. This revision addresses reviewer requests: explicit prob- lem statement, a concise state-of-the-art section, narrative bridging before mathematics, telemetry-based parameter estimation, a fully worked 4-node numeric example with embed- ded TikZ plots, and rigorous proofs (critical load, modal fragility, cascade).