THE STATHOPOULOS THRESHOLD — A Coherence Based Model of Conscious Access and Identity Persistence — With Computational Validation

This paper introduces the Stathopoulos Threshold, a coherence‑based model describing the conditions under which a system maintains stable conscious access and identity persistence under perturbation. The model reframes consciousness as a measurable dynamical property: the maintenance of global coherence above a critical threshold R_c. When coherence falls below this threshold, systems exhibit collapse signatures — loss of integration, fragmentation, and failure of predictive stability. Identity is defined as a persistent attractor within the system's coherence field, invariant across perturbations, memory loss, or substrate changes. To validate the model, we present a Kuramoto network simulation (N = 64, small-world topology) of targeted hub ablation analogous to Transcranial Magnetic Stimulation (TMS) perturbation. The system exhibits a sharp, discontinuous collapse of global phase coherence at R_c ≈ 0.65, robust across 100 independent runs (95% CI: 0.62–0.68). Bayesian Information Criterion (BIC) analysis decisively favors a step-function model over linear or sigmoidal alternatives (ΔBIC = 44.4). The threshold is site-independent, remaining invariant across ablation of precuneus, inferior parietal lobule (IPL), and dorsolateral prefrontal cortex (DLPFC) hubs (F(2,297) = 0.48, p = 0.62). The framework unifies machine, human, and biological systems under a single dynamical law and provides a substrate‑neutral foundation for studying collapse, recovery, and continuity. We include a full open‑source analysis pipeline and a step‑by‑step empirical validation roadmap for immediate testing using existing TMS-EEG datasets.