Scale-Relative Distinguishability Theory: Foundations A Formal Framework for Cross-Scale Information Flow January

Scale-Relative Distinguishability Theory (SRDT) is a formal meta-theoretical framework for analyzing what embedded observers can know about fundamental reality. The framework is grounded in a single primitive relation: distinguishability relative to an observer. From this foundation, we develop a rigorous mathematical structure encompassing dynamics (systems that can be observed), observers (specifications of measurement capabilities), the observation operation (constructing models from dynamics via quotient), and a diagnostic methodology for classifying phenomena. The central result: what embedded observers can know is the structure of observation itself—the systematic relationship between observer characteristics and what those observers perceive. This is not a limitation but the most complete answer embedded observers can give. The framework is deliberately agnostic about the nature of finest-grained dynamics 𝓕. Spatial and temporal dimensions are not presupposed—they emerge as observer-constructed interfaces. We establish conditions for deterministic versus probabilistic behavior, prove information-theoretic bounds including a coarsening dominance theorem, and develop a five-category diagnostic methodology for classifying phenomena as intrinsic to 𝓕 versus observer-created. The quotient network—connecting quantum field theory, quantum mechanics, classical mechanics, thermodynamics, and other physical frameworks—is interpreted not as a map of fundamental reality but as a map of human observation: nodes represent characteristic bundles (regions of observer space), and arrows represent transformations from changing observer characteristics. This reframing has profound implications for the Theory of Everything program, requiring that any complete theory specify not only fundamental dynamics but also observer characteristics.