Scale-Relative Distinguishability Theory - The Complete Knowledge Base: A Unified Framework for Observer-Relative Physics

Every physical theory is constructed by observers embedded within the system they describe. This embedding is not a limitation to be overcome — it is a structural feature that determines the form of all empirical knowledge. Scale-Relative Distinguishability Theory (SRDT) provides a rigorous mathematical framework for characterizing exactly what embedded observers can determine about fundamental dynamics, and what remains provably underdetermined. SRDT formalizes observation as a quotient operation. An observer O with finite resolution induces an equivalence relation on fundamental dynamics F, collapsing configurations that O cannot distinguish. What the observer perceives is the quotient F/∼O — not reality itself, but reality filtered through specific observational constraints. Different observers, with different resolutions and sensitivities, perceive different quotients of the same underlying dynamics. The framework delivers four principal results: A domain-independent formalism. SRDT provides a common algebraic language in which any physical theory can be expressed as a quotient of fundamental dynamics by observer limitations. Version 2. 0 introduces a formal quotient algebra with dimensional decomposition, support classification, and composition rules — making results from statistical mechanics, quantum field theory, general relativity, and condensed matter physics structurally comparable within a single mathematical framework. Precise determinacy conditions. Not all observational uncertainty is alike. Some features of fundamental dynamics are fully constrained by what we observe; others are provably underdetermined by any finite-resolution measurement. SRDT establishes exact conditions for when observations determine dynamics uniquely versus when genuine ambiguity persists — replacing informal appeals to underdetermination with rigorous, case-specific analysis. A diagnostic classification of phenomena. Is a given physical property intrinsic to fundamental dynamics, an artifact of observer limitations, or a structural feature that emerges only at coarse-grained scales? SRDT's five-fold classification (F-candidate, Observer-eliminated, Observer-created, Observer-selective, F-unity) provides systematic, reproducible answers — addressing longstanding questions about the status of thermodynamic irreversibility, wavefunction collapse, spatial locality, and the arrow of time. A constructive constraint set. Analysis of 19 major physics transforms — from quantum electrodynamics to classical electromagnetism, from quantum chromodynamics to nuclear physics, from field theory to cosmology — yields 148 constraint instances that compress to fewer than 25 independent generators. This constraint web eliminates four of six candidate classes of fundamental theory and narrows the viable solution space to UV completions of the Standard Model with diffeomorphism-invariant gravity. Version 2. 0 integrates the quotient algebra as load-bearing infrastructure throughout the knowledge base. Each transform analysis now includes dimensional decomposition, driving/derived classification, and compositional position within the full transform network. A Transform Registry consolidates algebraic metadata across all analyses, revealing cross-domain structural isomorphisms invisible to any single-domain treatment. SRDT is a meta-theoretic framework: it does not propose specific content about fundamental reality, but constrains what form any valid theory must take for observers like us. It characterizes the structure of the observation function P (O) — the mapping from observer characteristics to perceived physics — with mathematical precision. This is the most complete and epistemically honest answer that embedded observers can construct about the nature of fundamental reality.