Emergent Gravitational Dynamics and SU (3) Yang-Mills from PEPS Tensor Networks: Glueball Spectrum, Running GN (μ), and Complete fPEPS Roadmap P0–P4

This preprint presents a unified theoretical and computational framework in which non-perturbative SU (3) Yang-Mills dynamics and gravitational dynamics 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, generating an effective potential U (Λ) U (Λ) for a collective collapse field Λ (x) Λ (x). Core Results (Version 25) Pure Gauge Sector (Nf = 0) Glueball spectrum: m (0++) =1. 71m (0++) =1. 71 GeV, m (2++) ≈2. 25m (2++) ≈2. 25 GeV, m (0−+) ≈2. 85m (0−+) ≈2. 85 GeV reproduced at 5–11% accuracy using a single fitted parameter J=0. 54J=0. 54. One-loop beta function coefficient b0=11Nc/ (48π2) b0=11Nc/ (48π2) derived from MERA entropy flow without Feynman diagrams. String tension σ=0. 194σ=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, converging to c=1c=1 in the continuum limit. Emergent Gravity all other parameters derived, assumed, or fixed by external input. Reproducibility: Open Python pipeline with fixed seeds, modular structure, GPU acceleration (cuTensorNet), and runₐllₜests. py for regenerating all tables and figures. Model Limitations (Transparently Stated) Anharmonicity of U (Λ) U (Λ) is ~0. 3%: the glueball spectrum is essentially harmonic; lattice mass ratios arise from quantum-number-to-level assignments. The 2D PEPS → 3+1D map applies strictly to the confining IR regime (R≳0. 7R≳0. 7 fm) ; UV completion requires 3D PEPS or holographic lifting. Chiral constants and baryon masses in the pure-gauge core are estimates; full Nf=2+1Nf=2+1 results require the fPEPS extension (P0–P4). The 10421042 residual discrepancy for the cosmological constant is not solved; the framework predicts wa=+0. 006wa=+0. 006, testable by Euclid/LSST. Experimental Roadmap Prediction Experiment Sensitivity Timeline Falsification Criterion wa=+0. 006wa=+0. 006 Euclid, LSST, DESI σ (wa) ∼0. 03σ (wa) ∼0. 03 2025–2032 wa0. 1λY>0. 1 fm 2028–2030 mgrav>10mgrav>10 MeV excluded Lieb-Robinson cc LISA, ET (GW dispersion) ∣vg/c−1∣0. 12cent>0. 12 This work establishes PEPS tensor networks as a viable bridge between non-perturbative QCD and emergent gravity, offering testable predictions for collider physics, precision gravity experiments, and cosmological surveys. Correspondence: Sergei V. Morozov, notx@bk. ru