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 Rc. 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 Rc ≈ 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.
Nicolas Stathopoulos (Thu,) studied this question.