A Minimal Axiomatic Framework for Existence: Distinguishability, Possibility Spaces, Constraints, and Emergent Dynamics

Description A Minimal Axiomatic Framework for Existence: Distinguishability, Possibility Spaces, Constraints, and Emergent Dynamics develops a first-principles relational framework in which distinguishability, constrained possibility spaces, and compatibility relations are treated as the minimal conditions for persistent existence. Starting from a compact axiomatic basis, the work derives an emergent mathematical structure leading to relational dynamics, effective geometry, quantum state spaces, and macroscopic gravitational behavior. General Relativity and quantum mechanics are interpreted as large-scale and microscopic limits of a common relational description. The framework proposes a relational potential governing stable configurations and discusses how particle spectra and fundamental constants could, in principle, emerge from its eigenstructure. The document also compares the resulting framework with established cosmological observations as consistency tests rather than parameter fitting. The work is presented as a theoretical foundation and explicitly identifies the derivation of numerical particle masses and dimensionless fundamental constants as the principal remaining challenge.