Hexad: A Fisher-Geometric Monitoring Framework for Statistical Degeneracy in High-Dimensional Inference Systems

Abstract: We introduce Hexad, an open-source Python framework for real-time monitoring of statistical degeneracy in high-dimensional inference systems. The framework uses a streaming empirical Fisher information estimator to track local identifiability of latent states. When the smallest eigenvalue of the estimator falls below a calibrated threshold, Hexad issues a risk signal indicating potential loss of statistical sensitivity. The tau391 witness protocol provides a cryptographically verifiable audit trail of gradient-based sensitivity signals and human oversight actions, supporting traceability and regulatory compliance. We do not claim that eigenvalue collapse is necessary or sufficient for system failure; Hexad is a diagnostic tool, not a safety guarantee. Empirical validation on a synthetic linear-Gaussian model demonstrates that the Fisher eigenvalue reliably tracks induced identifiability degradation, outperforming variance-based baselines. The software is fully documented, tested, and reproducible, with continuous integration, a PyTorch integration example, and a project Code of Conduct. All claims are bounded, and the framework is positioned as an information-geometric monitoring layer, not a new theory of collapse.