The Tateonian Framework: A Mathematical Exploration Toward a Unified Theory of Spacetime, Information, and Emergence

This paper introduces the Tateonian Framework, an exploratory mathematical approach to understanding how physical reality, spacetime, information, and complex systems may emerge from fundamental relationships and interactions. The framework investigates whether apparently separate scientific mysteries may share underlying mathematical principles. It proposes a multiscale model in which events, relational possibilities, actual interactions, information accessibility, accumulated history, and the emergence of higher-order structures are distinguished and tracked across organizational layers. The paper develops mathematical formulations addressing relational geometry, reciprocal interactions, generative conditions, the emergence of physical time, cross-layer information transfer, and the conditions under which interacting components may form persistent, autonomous systems. Potential applications include foundational questions in quantum physics, quantum gravity, the nature of time, complex systems, and the origin of organized physical structures. Particular attention is given to the distinction between what exists within a complete system and what can be observed or reconstructed from a limited perspective. Rather than claiming to resolve these longstanding scientific problems, the paper offers a mathematical framework for investigating them from a unified relational perspective, identifying testable hypotheses, unresolved questions, and possible connections to established theories. The work is presented as an invitation to scientific examination, further mathematical development, independent testing, and interdisciplinary collaboration.