Emergent Gravitational Dynamics and SU(3) Yang-Mills from PEPS Tensor Networks: Glueball Spectrum, Einstein Identity, Neutrino Masses, and 22-Test Verification Suite

This preprint presents a unified theoretical and computational framework in which non-perturbative SU (3) Yang-Mills dynamics, gravitational dynamics, and neutrino phenomenology emerge from a single Projected Entangled Pair State (PEPS) tensor network. The QCD vacuum is modeled as a gauged PEPS on a 2D lattice combined with a Multiscale Entanglement Renormalization Ansatz (MERA) modular Hamiltonian. Core Results (Version 26) Pure Gauge Sector (Nf = 0) Glueball spectrum reproduced at 2. 6–11. 3% accuracy using a single fitted parameter J = 0. 54 One-loop beta function coefficient b₀ = 11Nc/ (48π²) derived from MERA entropy flow without Feynman diagrams String tension σ = 0. 194 GeV² from area-law entanglement entropy, consistent with lattice QCD Speed of light derived as the Lieb-Robinson velocity of the PEPS network Emergent Gravity Σm_ν = 62. 5 meV testable by CMB-S4 Fermionic PEPS: Complete Roadmap P0–P4 P0: Gap equation → dynamical chiral symmetry breaking, f_π = 92. 4 MeV P1: Fermionic PEPS with Grassmann variables, sign-problem handling P2: String breaking as topological transition, Rbreak = 0. 68 fm P3: Direct extraction of ⟨q̄q⟩, GMOR verified to 2–5% P4: Full GPU-accelerated pipeline, phase diagram prediction 22-Test Verification Suite 19 of 22 tests have deviation 0. 1 fm 2028–2030 mgrav > 10 MeV δCP ≈ −87° DUNE, T2HK σ (δCP) ~ 10° 2028–2032 δCP −50° Σm_ν ≈ 62. 5 meV CMB-S4 σ (Σm) 100 meV This work establishes PEPS tensor networks as a viable bridge between non-perturbative QCD, emergent gravity, and neutrino phenomenology, offering testable predictions for collider physics, precision gravity experiments, and cosmological surveys. Correspondence: Sergei V. Morozov, notx@bk. ru