The Geometry of Criticality: Residual Hessian as a Detector of Precursory Silence in Synthetic SOC Systems

In the framework of Computational Epistemology, we distinguish between two types of model failure: narrative overfitting (artificial smoothing of noise) and structural blindness (when a model fails due to an underlying phase transition). In this publication, we test the latter using the Olami-Feder-Christensen spring-block model, a canonical representation of Self-Organized Criticality. We apply a non-negative regularized linear operator within a sliding window and analyze the geometry of the residual Hessian. Our synthetic experiments demonstrate that macro-avalanches are preceded by a distinct collapse in the residual autocorrelation roughly 1,000 steps before the event. We interpret this as "precursory silence": the moment when linear memory is lost, and the system transitions from critical slowing down to deterministic rupture. This note establishes the residual Hessian as a domain-agnostic mathematical detector for critical transitions.