Emergent Fundamental Constants and Particle Mass Generation from the Entropic–Lagrangian Framework

The Entropic-Lagrangian Framework (ELF) derives all physics from two primitive counterpropagating scalar fields σ (entropic) and ξ (Lagrangian) whose interference generates spacetime, forces, and matter.We present five results obtained from a single governing action with zero free parameters beyond the electron mass anchor.(i) The speed of light c emerges as the vacuum phase velocity of σ-ξ alignment events.(ii) The fine-structure constant α is derived by two independent geometric methods-a combinatorial lattice formula and a phase-space self-referential fixed-point analysis-both converging on αELF = 0.007 297 356 2, agreeing with the CODATA value 0.007 297 352 569 3 to six significant figures.(iii) The Schrödinger equation, Einstein field equations, and second law of thermodynamics are recovered as limiting cases of the unified evolution rule.(iv) Lepton and baryon masses are eigenvalues of the σ-ξ interference operator Zn = |n 2 sin(nθ)| with θ = arcsin √ α, reproducing the electron, muon, tau, proton, and neutron to better than 0.1% with no free parameters.(v) The neutron-proton mass splitting is reproduced to 0.05% by two sequential viscosity corrections encoding the lattice impedance ηL and the neutron half-life t 1/2 .A falsifiable prediction-a differential clock rate δR ≈ -7 × 10 -18 between Al + and Sr optical clocks-is accessible with existing NIST instrumentation.