Fractal-Restricted Yang–Mills Theory with Fermions

This repository contains the complete dataset and analysis scripts for the groundbreaking study "Fractal-Restricted Yang-Mills Theory with Fermions", which proposes a novel approach to non-perturbative QCD phenomena. Key features include: Theoretical Framework: Rigorous formulation of fractal-restricted Yang-Mills theory with an innovative fractal-scaling operator FαFα. Dynamical coupling of fermions via an auxiliary scalar field σ(x)σ(x) to ensure numerical stability. Key Results: First-principles prediction of a positive mass gap (Δ>0Δ>0), addressing a Clay Millennium Problem. Precision calculations of hadron masses: Pion (132±15132±15 MeV) and Rho (810±50810±50 MeV) matching experimental values within 7%. Provocative heavy glueball prediction (2608±7102608±710 MeV) challenging conventional QCD estimates. Dynamical chiral symmetry breaking with condensate ⟨ψˉψ⟩=−(210±35 MeV)3⟨ψˉψ⟩=−(210±35 MeV)3. Numerical Implementation: Lattice QCD simulations on 8484-164164 grids with staggered fermions. Full parameter sets (γ=0.5γ=0.5, λσ=0.05λσ=0.05, etc.) and Monte Carlo configurations. Scripts for correlation function analysis and mass gap extraction (Python/Julia). Experimental Implications: Direct testable predictions for glueball searches at GlueX, BESIII, and LHCb. Dataset serves as benchmark for future fractal-QCD studies.