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 (N_f = 0) Glueball spectrum reproduced at 2.6–11.3% accuracy using a single fitted parameter J = 0.54 One-loop beta function coefficient b₀ = 11N_c/(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 & RG Flow Running Newton constant: G_N(μ) = 1/[4·c_ent·μ²·b₀·ln(μ/Λ_QCD)] with c_ent ≈ 0.095 reproduces the physical value at the Planck scale The historical 10³⁸ hierarchy resolved as genuine RG running driven by vacuum entanglement entropy Massive emergent graviton m_grav = 85 MeV with Yukawa range λ_Y = 2.3 fm, fully compatible with all fifth-force constraints Einstein Identity Theorem [NEW v26] For any SU(3)-invariant fermionic PEPS, the renormalized energy-momentum tensor equals the Ricci curvature constructed from entanglement gradients: T_μν = f(η/s)·R_μν + O(χ⁻¹) Numerical verification: R_μν/T_μν → 8πG_eff with systematic error decreasing as 1/(χ ln χ), reaching 2.6% at χ=32 Neutrino Sector [NEW v26] PMNS mixing angles and CP phase predicted from tensor network geometry: δ_CP = −86.8° (pull = +0.03σ) without free parameters Neutrino mass spectrum from entanglement entropy power law: m_i = Λ*·[−ln(F_i)]³ with Λ* = 7.387×10⁻⁴ eV Normal mass ordering predicted from topology; 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, R_break = 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 <10%; 3 neutrino tests are new predictions Transparent error budget: parametric / systematic / total uncertainties (68%/95% CI) Open Python pipeline with fixed seeds, modular structure, run_all_tests.py Model Limitations (Transparently Stated) Anharmonicity of U(Λ) is ~0.3%; higher glueball states require multi-gluon operators 2D PEPS → 3+1D map applies to confining IR regime; UV completion requires 3D PEPS Chiral constants in pure-gauge core are estimates; full N_f=2+1 results require fPEPS extension Cosmological constant residual discrepancy 10⁴² not solved; framework predicts w_a = +0.006 Experimental Roadmap Prediction Experiment Sensitivity Timeline Falsification w_a = +0.006 Euclid, LSST σ(w_a) ~ 0.03–0.04 2025–2035 w_a < −0.05 m_grav = 85 MeV MAGIS-100 λ_Y > 0.1 fm 2028–2030 m_grav > 10 MeV δ_CP ≈ −87° DUNE, T2HK σ(δ_CP) ~ 10° 2028–2032 δ_CP < −120° or > −50° Σm_ν ≈ 62.5 meV CMB-S4 σ(Σm) < 15 meV 2027–2030 Σm_ν > 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