Maximum Entropy Production Framework: A Unified Theory of Fundamental Constants, Cosmology, and Particle Physics

Maximum Entropy Production Framework from S3S^{3}S3 Topology Version 7.9 — Trajectory-Typicality / Ensemble-Dependent Extremum Edition This document develops a micro-founded nonequilibrium framework in which the observed macroscopic history is selected by trajectory typicality: under coarse-graining of quantum dynamics for an open system, path probabilities concentrate around histories that extremize an ensemble-dependent functional. In this formulation, “MEP” is not asserted as a universal MaxEP slogan; rather, it appears as a controlled reduction of a more general large-deviation / maximum-caliber statement, with the sign of the extremum (max vs min) determined by the control ensemble (force-controlled vs flux-controlled, boundary conditions, reservoir couplings). Within this principled setting, we propose a specific geometric realization in which the relevant state space and constraint structure are encoded by S3S^{3}S3 topology (and its discrete symmetry/holonomy data). The central claim is that, once the ensemble is specified and the admissible macrostates are fixed by the topology, a large class of dimensionless quantities are determined without tunable parameters. The framework is developed to be explicitly falsifiable: it yields concrete numerical targets (and uncertainty budgets when appropriate) that can be confronted with present data and future measurements. Scope of results. The manuscript assembles a unified “ledger” of predictions spanning particle physics (including mixing and CP structure), precision couplings, and selected cosmological observables. Where approximations are used, they are stated as assumptions and separated from the core variational/typicality logic. Particular attention is paid to known failure modes of naive MaxEP claims—near-equilibrium convex regimes, trivial uniqueness, metastability/hysteresis, symmetry-degenerate branches, and nonstationary attractors—by making the domain of validity explicit and by keeping the framework at the trajectory-functional level where these cases are naturally accommodated. Status and intent. This is independent theoretical work and should be read as a research program: a coherent derivation pathway, a collection of falsifiable numerical consequences, and a set of clearly identified theoretical gaps. A companion manuscript (“MEP as a Consequence of Quantum Mechanics”) provides the microscopic route via influence-functionals and large-deviation theory; the present document focuses on the S3S^{3}S3 geometric instantiation and the resulting phenomenological ledger. Keywords: trajectory typicality; large deviations; maximum caliber; ensemble dependence (force vs flux); nonequilibrium steady states; S3S^{3}S3 topology; holonomy; dimensionless constants; mixing matrices; CP violation; cosmological constraints.