A Deterministic Limit for Catastrophic Tectonic Rupture: Deriving the Critical Asperity Nucleation Length via Spatiotemporal Stress Diffusion

The forecasting of catastrophic seismic events remains heavily reliant on probabilistic hazard models, such as the Gutenberg-Richter relationship and empirical Coulomb stress transfer approximations. While classical Dieterich-Ruina rate-and-state friction (RSF) laws describe the localized evolution of fault slip, they struggle to deterministically define the exact spatiotemporal boundary where stable aseismic creep transitions into dynamic, runaway rupture. This paper introduces a non-local continuum framework for tectonic stress scaling. By modeling the seismogenic zone as a thermodynamic balance between the elastic delocalization of crustal shear stress and the localized dissipation of frictional state memory, we derive a universal critical nucleation length (Lcrit). We demonstrate that catastrophic tectonic rupture is an exact deterministic limit where localized frictional decay strictly overpowers the elastic stress-redistribution capacity of the surrounding crust. We contrast this invariant with traditional probabilistic hazard forecasting and propose a blueprint for Active Tectonic Monitoring (ATM) utilizing distributed acoustic sensing (DAS).