The Three Sphere Model (TSM) of Consciousness: Informational Phase Transitions and the Cognitive Event Horizon

This paper introduces the Three Sphere Model (TSM), a dynamic framework for quantifying consciousness through the integration of internal (Ai), environmental (Ae), and social (As) information domains. While contemporary models, such as Integrated Information Theory (IIT), focus on neural substrates, TSM formalizes consciousness as a resultant Euclidean vector norm in a three-dimensional information space. By applying the integration formula Atotal(t) = (αAi) 2+ (βAe) 2+ (γAs) 2, TSM treats thought processes as informational tokens broadcast across these cognitive boundaries. To validate the model, a computational simulation using Ordinary Differential Equations (ODEs) was conducted, incorporating a novel Social Contagion Index (Γ) and an Exhaustion Penalty (Ω). Our results identify a critical "Cognitive Event Horizon" at t≈5.2, a fundamental phase transition where the system’s integration metric (Φproxy) shifts from positive to negative. We demonstrate that this transition represents the threshold where the computational cost of maintaining a unified self-model exceeds systemic capacity, forcing a shift from integrated, reflective awareness to distributed, specialized informational processing. This architecture offers a scalable framework for both biological cognitive science and the design of robust, stable Artificial General Intelligence (AGI), providing a mathematical basis for predicting the point of systemic dissolution in high-density informational environments.