Lattice Index Theorem Validation in ICC Framework (Gravitational Wave Predictions)

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]. ## NEW IN VERSION 3.0: Gravitational Wave Predictions Based on the lattice-validated topological index fluctuations (⟨ν²⟩ ≈ 3.6), the ICC framework predicts a stochastic gravitational wave background detectable by multiple experiments: | Band | Frequency | h²Ω_gw | Experiment | Detectability ||------|-----------|--------|------------|---------------|| PTA | 1e-8 Hz | 2.4e-10 | NANOGrav | Consistent with 15yr signal || PTA | 1e-9 Hz | 2.6e-13 | SKA | Detectable || LISA | 1e-3 Hz | 2.4e+05 | LISA | Strongly detectable || Ground | 10-1000 Hz | <1e-9 | LIGO | Below current bounds | ## Key Results (Version 3.0) - **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- **Gravitational waves**: Complete spectrum from nHz to kHz bands ## Archive Contents (7 files) 1. `icc_v3_part1.tar.gz` - README, FINAL_REPORT, LaTeX preprint2. `icc_v3_part2.tar.gz` - Main Python scripts (SU(2), SU(3), anomaly, curvature)3. `icc_v3_part3_gw_scripts.tar.gz` - GW simulation scripts (7 Python files)4. `icc_v3_plots_su2.tar.gz` - SU(2) spectral flow and scaling figures5. `icc_v3_plots_su3.tar.gz` - SU(3) spectral flow figures6. `icc_v3_plots_anomaly.tar.gz` - Chiral anomaly and curvature correlation7. `icc_v3_plots_gw.tar.gz` - Gravitational wave spectra (3 figures) ## Reproducibility - Python 3.9+ required- Dependencies: numpy, matplotlib, scipy- Quick start: `python su2_index_flow.py --q=2 --L=12 --delta=0.1`- GW simulation: `python track4_gw/gw_spectrum_complete.py` ## Citation ```bibtex@software{gimranov_2026_20198997, author = {Gimranov, Alik}, title = {Lattice Index Theorem Validation in ICC Framework (Gravitational Wave Predictions)}, version = {3.0}, doi = {10.5281/zenodo.20198997}, year = {2026}}