Layer-Dependent Information and Emergence: Computational Tests of the Tateonian Framework

This paper presents a series of mathematical and computational investigations into the Tateonian Framework, an exploratory relational approach to understanding spacetime, information, physical organization, and emergence across multiple scales. Building upon the theoretical foundations developed in Paper I, this study examines how information, causal relationships, physical interactions, and organizational structures behave when viewed at different levels of a system. The investigations include quantum entanglement and globally distributed information, reduced-state dynamics, causal ordering and the emergence of time, multiscale feedback, autocatalytic persistence, relativistic consistency, and mathematical constraints relevant to the Yang–Mills mass-gap problem. A central question explored throughout the paper is whether the observable behavior of a system can be fully understood from its individual components, or whether relationships, accumulated histories, and higher-order organization contain essential information that becomes inaccessible when examined at a smaller scale. The computational experiments identify important distinctions between actual events and observed events, structural connections and persistent organization, locally accessible information and globally distributed information, and mathematical descriptions of a system at different scales. Although several findings reproduce established mathematical results, they provide useful benchmarks and constraints for developing and evaluating the Tateonian Framework. The paper distinguishes these established results from proposed extensions and identifies where further mathematical derivation and independent testing are required. Potential areas of application include quantum foundations, emergent spacetime, the nature of physical time, quantum information, complex systems, self-organization, and mathematical physics. The purpose of this research is not to claim that these longstanding scientific problems have been solved, but to investigate whether a unified relational perspective may reveal useful connections, identify limitations in simplified descriptions, and provide new directions for scientific inquiry. The work is offered for independent examination, critical testing, further mathematical development, and interdisciplinary collaboration.