Latent Geometry as a Structural Monitor: Eigenspace Alignment for Anomaly Detection in Anonymity Networks

TL;DR

This paper introduces a geometric approach to anomaly detection in networks, focusing on structural organization as a precursor to observable behavior changes, validated on the Tor network with high accuracy.

Contribution

It presents a novel structural-monitoring framework using eigenspace alignment to detect anomalies before geometric signals manifest.

Findings

Identified a stable nine-dimensional subspace in Tor network data.

Achieved zero false positives on stable observation windows.

Falsified the relay-departure hypothesis during a network event.

Abstract

Traditional anomaly detection marks events when measured signals cross predefined thresholds. This captures the moment of transition but not the structural pressure that precedes it. We propose treating large behavioral populations as geometric energy landscapes whose deformation can be measured before and during major transitions. The central thesis is that structure precedes geometry: the structural organization of the population is the signal, and geometric metrics are instruments for measuring it. Applied to the Tor anonymity network across 67 consecutive daily observation windows, the dual-observer pipeline identifies a stable nine-dimensional load-bearing subspace invariant across the observation period and validates this structure by Monte Carlo simulation at 16.8 sigma above the noise floor. Primary detection gates achieve 0.0% false positive rate on 24 confirmed stable windows. Forensic analysis of the February 20, 2026 confirmed infrastructure event formally falsifies the relay-departure hypothesis, identifying connectivity degradation without topology change as a detectable network failure mode. The result is a candidate structural-monitoring framework for behavioral populations with sufficient telemetry.