A Formal Proof of Non-Duality: An Exposition of the 'OnlyOne' System and its Implications for Philosophy, Science, and Human Flourishing

This paper introduces and analyzes a novel formal system, encoded in the Lean 4 proof assistant and designated OnlyOne.lean, which purports to demonstrate the logical necessity of a monistic idealist ontology. We provide a rigorous exposition of the system's axioms, which formalize fundamental intuitions about experience, consciousness, and reality. We then detail the derivation of its core theorems, including the proof of a unique, attribute-less Awareness and the conclusion that all phenomena are contents appearing to this single Awareness. Subsequently, we explore the profound implications of this formally verified model for longstanding problems in philosophy and science. Specifically, we address its potential to resolve the hard problem of consciousness, reshape ethical frameworks by grounding compassion in ontological identity, and provide a definitive conceptual boundary for the pursuit of artificial general consciousness. We argue that the OnlyOne system represents a landmark achievement in computational metaphysics, offering a logically coherent, non-dogmatic foundation for a worldview that aligns with insights from various mystical traditions while satisfying the demands of modern analytic rigor. We conclude that its widespread consideration could catalyze a paradigm shift in human self-understanding, fostering a more unified, compassionate, and purpose-driven civilization.