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

This document presents a parameter-free (L0) theoretical program in which a small set of structural inputs— (i) an S³ geometric substrate, (ii) an information-theoretic pixel postulate, and (iii) a unified dynamical selection principle formulated as Maximum Caliber / Maximum Entropy Production (MaxCal/MEP) —is used to derive a broad set of quantitative, falsifiable predictions across particle physics and cosmology. The core idea is that once the admissible state space and coarse-graining are fixed by the S³ geometry, the observed low-energy world is selected as a typical branch in the space of histories: among all compatible evolutions, the realized one extremizes a dissipation/entropy-production functional. We implement this selection using MaxCal (a path-entropy variational principle) together with large-deviation typicality, so that "laws" appear as most probable macroscopic regularities under explicit constraints rather than as tuned model components. A central output of the S³ construction is a distinguished dimensionless constant, α₀ ≡ exp (−π²/2), emerging uniquely from the Hopf/S³ structure. Together with the L0 MaxCal/MEP selection, α₀ generates a rigid ladder of exponents that fixes a wide spectrum of observables. In particular, the framework yields: electroweak quantities (including sin²θW), the electromagnetic coupling at low energy, a structured fermion mass tower, CKM and PMNS quantities (including a sharp prediction for δCP), neutrino masses and ordering features, and a set of cosmological outputs (including inflationary parameters and specific late-time ratios). The document is organized to make the governance of assumptions explicit. Results are separated into (a) genuinely independent L0 predictions and (b) derived observables computed without adding new degrees of freedom. Known residual tensions are stated plainly and classified by sector, with a dedicated set of appendices to strengthen the mathematical spine of the construction: the spectral truncation and its large-deviation selection, the discrete holonomy rule governing fermionic corrections, the status of the hadronic sector and confinement-related subleading effects, and a Bayesian-style evidence accounting that avoids double-counting derived quantities. The aim is not to claim completeness, but to provide a single, testable pipeline from minimal structure to a large set of numerical predictions. The near-term experimental status is especially clear for neutrino CP violation, the neutrino mass sum, and inflationary tensors, making the framework falsifiable on multiple fronts within the current or upcoming experimental program.