The Living Audit: Collapse, Memory, and Universal Mathematics in Empirical Fields

This work establishes a unified, operational mathematics of audit, collapse, and recursive memory across the empirical sciences. Integrating quantum physics, nanomedicine, biological systems, and field theory, the Universal Mathematics & Collapse Platform (UMCP) provides a regime-based framework for measurement, anomaly detection, and calibration in complex systems. The study develops new invariants—drift, fidelity, entropy, curvature, reentry delay, and composite integrity—that diagnose regime boundaries and enable dynamic, cross-domain audit protocols. Through a series of case studies—including quantum interference (double-slit), gut-brain field signaling, stereoisomeric nanomedicine, and THz liquid collapse—the paper demonstrates that collapse is not a singular event, but a generative process: boundaries and anomalies are reinterpreted as sites of renewal, memory, and adaptive repair. All protocols, data, and canonical operator logic are made openly available for reproducibility and further application. This work is both a comprehensive record of field-tested mathematics and a blueprint for extending recursive audit to new domains.