Spectral Resiliency Index: A Finite-Element Inspired Framework forPredictive Fragility Analysis in Distributed Computing Systems
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Abstract
Resilience in distributed computing systems is often measured reactively through chaos engineering or
stress testing. We propose a predictive, non-invasive framework based on eigenvalue analysis of telemetry-
driven system matrices. Inspired by finite-element dynamics, we define analogues of mass, stiffness, and
damping matrices in computing systems, and derive the Spectral Resiliency Index (SRI) as a stability
metric. We establish theorems, proofs, and corollaries connecting eigenvalue spectra to fragility zones.
Using open Grafana/Prometheus telemetry datasets, we demonstrate 3-tier and microservice architectures,
with TikZ/PGFPlots visualizations of fragility heatmaps. Results show that SRI reveals hidden fragility
zones and anticipates system failures, outperforming reactive approaches
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