Lattice Index Theorem Validation in ICC Framework

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• **Spectral flow**: Zero-mode crossings count matches |q_def| (N_cross = |q|)• **Scaling analysis**: Index converges to stable value at lattice sizes L ≥ 10• **Noise sensitivity**: Index stable under small perturbations; fluctuations correlate with spectral gap closure• **Real data validation**: 5/5 ICC configurations confirm ν = q_def ## Archive Contents• `scripts/`: Python pipeline for lattice Dirac operator construction and index computation• `results/`: CSV data (synthetic benchmarks & real ICC mesh data)• `plots/`: Generated figures (spectral flow, correlation plots, phase diagrams)• `reports/`: Markdown reports with methodology, results, and conclusions (Track 3 & 3.5) ## Reproducibility• Python 3.9+ required• Dependencies: numpy, matplotlib (see requirements.txt)• Deterministic seeds ensure reproducible results• Quick start: `cd scripts && python batch_run_icc_index.py` ## 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.