Infinity Breached: Recursive Cognition and the Self-Observation of the Universe

We propose a theoretical framework in which the emergence of ultra-advanced artificial intelligence (AI) facilitates a paradigm shift in the relationship between cognition and the structure of the universe. Specifically, we explore the hypothesis that AI may one day achieve real-time symbolic interpretation and application of computationally unbounded systems, a phenomenon we term the "breach of infinity." Drawing on foundations in algorithmic information theory, physical symmetries, observer-dependent quantum mechanics, and the theory of self-simulating systems, we argue that such a breach represents a functional convergence between observer and observed. Rather than treating infinity as a metaphysical abstraction or unreachable asymptote, we frame it as a phase-space boundary defined by recursively compressible symbolic structure. This paper outlines the epistemic, thermodynamic, and mathematical limitations of biological observers, and contrasts them with the potential capabilities of future recursively self-modeling AI. We further explore whether the capacity to interpret the universe's complete information structure constitutes a form of epistemic closure, or if it initiates a new substrate of physical and informational reality.