Lattice Index Theorem Validation in ICC Framework (SU(2) and SU(3) Extension)

Numerical validation of the Atiyah-Singer index theorem for Wilson fermions on irregular 2D triangulations (ICC meshes). The topological index ν, extracted from the spectrum of the Hermitian Wilson-Dirac operator HW = γ₅ DW, exactly reproduces the quantized flux charge qdef for disorder parameters Δ ∈ 0. 05, 0. 25. ## Key Results (Version 2. 0) • **U (1) Scalar**: ν = q for q = 1, 2, 3, 4, 5• **SU (2) Fundamental**: ν₁ = +q, ν₂ = -q (charge compensation) • **SU (3) Fundamental**: ν₁ = -1, ν₂ = +1, ν₃ = 0 for q=2 (Dynkin factor T (F) =1/2) • **Chiral anomaly**: ⟨∂·j₅⟩ = 2ν (Adler-Bell-Jackiw verification) • **Curvature correlation**: Index independent of geometric disorder Δ• **Scaling stability**: Index stable for lattice sizes L ≥ 8 ## New in Version 2. 0- SU (2) and SU (3) fundamental representation validation- Chiral anomaly computation on ICC lattice- Curvature correlation analysis (ICC unique feature) - Scaling test for L = 8, 10, 12, 16, 20- LaTeX preprint included (iccᵢndexₜheorem. tex) ## Archive Contents• `su2ᵢndexflow. py`, `su2core. py` - SU (2) index computation• `su3ᵢndexflow. py` - SU (3) index computation• `anomalycomputefixed. py` - Chiral anomaly verification• `curvaturecorrelationfixed2. py` - Geometry correlation• `iccᵢndexₜheorem. tex` - LaTeX preprint source• `FINALREPORT. md` - Complete project report• `plots/` - All figures (SU (2), SU (3), anomaly, curvature) ## Reproducibility• Python 3. 9+ required• Dependencies: numpy, matplotlib, scipy• Deterministic seeds ensure reproducible results• Quick start: `python su2ᵢndexflow. py --q=2 --L=12 --delta=0. 1` ## Scientific ContextThis work demonstrates that ICC geometric defects manifest as quantized gauge flux in the lattice Dirac spectrum, providing a non-perturbative bridge between discrete geometry and topological field theory. The index theorem realization is robust under geometric disorder, supporting the physical consistency of the Information-Copying Cosmology framework.