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 H_W = γ₅ D_W, exactly reproduces the quantized flux charge q_def 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 (icc_index_theorem.tex) ## Archive Contents• `su2_index_flow.py`, `su2_core.py` - SU(2) index computation• `su3_index_flow.py` - SU(3) index computation• `anomaly_compute_fixed.py` - Chiral anomaly verification• `curvature_correlation_fixed2.py` - Geometry correlation• `icc_index_theorem.tex` - LaTeX preprint source• `FINAL_REPORT.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 su2_index_flow.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.