Spectral Signatures of Distributed Software Systems: Eigenvalue Profiling for Enterprise-Scale Proactive Resilience Engineering

Abstract

This paper develops a rigorous spectral framework for profiling distributed software systems at enterprise
scale. We represent a distributed system as a discretized assemblage of computational elements and
construct complexity- aware stiffness and mass matrices. By performing spectral decomposition of the
resulting generalized eigenproblem, we extract spectral signatures — normalized sets of eigenvalues and
derived statistics — which uniquely characterize system resilience, bottlenecks, and failure propagation
dynamics. We define a Spectral Resilience Index (SRI) and vertical-grade functions for different enterprise
domains (finance, healthcare, retail, telco). To improve robustness and adaptivity, we overlay a Hidden
Markov Model (HMM) that maps observed telemetry to latent resilience states and refines deterministic
spectral predictions. We validate the methodology using public datasets (DORA metrics, Death Star Bench
traces, and Google SRE reports), present synthetic and trace-driven examples, and show how spectral
fingerprints can be used for early-warning, prediction, and proactive resilience engineering — reducing the
need for ad-hoc chaos engineering