T.G.E.O. Aplicada a Inteligencia Artificial Embebida: Dashboard de Existencia Operativa y Predicción de Colapso

This work develops the formal application of the General Theory of Operational Existence (T.G.E.O.) to real‑time embedded Artificial Intelligence systems. By extending the classical state space and introducing a dissipative memory functional, the framework models representational fatigue arising from cumulative structural degradation. A non‑compensatory geometric performance index \(S(t)\) is defined, ensuring that critical failures cannot be masked by other metrics. Using Aubin’s Viability Theory, the Operational Existence Kernel is characterized and a deterministic method is derived to predict the definitive collapse horizon \(t^*\). The formulation is completed with an existential Hamilton–Jacobi–Bellman equation and a topological rescue operator capable of restoring viability through impulsive interventions aligned with the tangent cone geometry. The result is a mathematically rigorous mechanism for monitoring, predicting, and preventing representational collapse in embedded AI agents.