🤖 AI Summary
This study addresses the limitations of traditional anomaly detection methods, which focus solely on threshold-exceeding signals and fail to capture structural stress preceding critical events. The authors propose a latent-geometry-based structural monitoring framework that models large-scale behavioral ensembles as geometric energy landscapes, enabling early warning through the detection of structural deformations—embodying the core principle that “structure precedes geometry.” Applied to the Tor network, the method identifies a stable nine-dimensional support subspace and reveals, for the first time, a novel detectable failure mode: connectivity degradation without topological change. By integrating a dual-observer pipeline, subspace alignment, Monte Carlo simulation, and high-dimensional geometric analysis, the approach achieves a 0.0% false positive rate across 24 stable observation windows and attains a 16.8σ significance level in retrospective analysis of the infrastructure event on February 20, 2026.
📝 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.