ICC v3.2: Lattice-Validated Topological Index Fluctuations Predict a Detectable Stochastic Gravitational Wave Background

# ICC v3.2: Lattice-Validated Topological Index Fluctuations Predict a Detectable Stochastic Gravitational Wave Background ## Version 3.2 (May 2026) **Author:** Alik Gimranov (ORCID: 0009-0001-5952-9887) **DOI:** 10.5281/zenodo.20198997 (this DOI always resolves to the latest version) --- ## Abstract We present version 3.2 of the Information-Copying Cosmology (ICC) framework, wherein topological index fluctuations ⟨ν²⟩ arising from Wilson fermions on irregular 2D simplicial complexes generate a stochastic gravitational wave background (SGWB). Calibrated against NANOGrav 15-year pulsar timing data, the framework yields ⟨ν²⟩ = 3.6 ± 0.12 and a spectral index γ_eff = 3.9. The resulting spectrum Ω_GW(f) = Ω₀(f/f₀)5-γ_eff is fully compatible with CMB-S4 constraints on effective neutrino degrees of freedom (ΔN_eff = 0.05092 < 0.06). ICC v3.2 predicts strongly detectable signals across multiple observational bands: Ω_GW = 2.05×10⁻⁵ at 0.3 mHz (LISA), 7.83×10⁻¹⁰ at 30 nHz (SKA), and 5.80×10⁻³ at 0.1 Hz (DECIGO). We formulate four explicit falsification criteria that will test the framework with upcoming multi-messenger data. --- ## Key Parameters | Parameter | Value | Description ||-----------|-------|-------------|| Ω₀ | 2.40 × 10⁻¹⁰ | GW amplitude at f₀ = 10⁻⁸ Hz || γ_eff | 3.9 | Spectral index || ⟨ν²⟩ | 3.6 ± 0.12 | Topological index fluctuations (NANOGrav calibrated) || ΔN_eff | 0.05092 | Effective neutrino degrees of freedom (CMB-S4 compatible) | --- ## Predictions for Gravitational Wave Detectors | Detector | Frequency | Ω_GW(f) | Expected Status ||----------|-----------|---------|------------------|| **SKA** (Square Kilometre Array) | 30 nHz | 7.83 × 10⁻¹⁰ | Detectable (Hellings-Downs correlation) || **LISA** (Laser Interferometer Space Antenna) | 0.3 mHz | 2.05 × 10⁻⁵ | Strongly detectable || **DECIGO** (Deci-hertz Interferometer Gravitational Wave Observatory) | 0.1 Hz | 5.80 × 10⁻³ | Strongly detectable | --- ## Falsification Criteria ICC v3.2 is considered **falsified** if **ANY** of the following conditions are met by observational data: 1. **LISA null detection:** No SGWB signal in the 0.1-10 mHz band with Ω_GW < 10⁻¹² after 2 years of integration. 2. **SKA Hellings-Downs violation:** Absence of quadrupolar spatial correlation in the 1-100 nHz band, ruling out a cosmological SGWB origin. 3. **CMB-S4 tight bound:** Measurement of ΔN_eff < 0.01 while the NANOGrav signal remains consistent with ⟨ν²⟩ = 3.6. 4. **Spectral slope deviation:** High-precision spectral index measurement yielding γ_eff ∉ [3.7, 4.1], inconsistent with the f1.1 scaling derived from ⟨ν²⟩ fluctuations. --- ## File Contents | File | Description ||------|-------------|| `ICC_v3.2_manuscript.pdf` | Full manuscript in PDF format || `manuscript.tex` | LaTeX source of the manuscript || `references.bib` | BibTeX bibliography || `ICC_v3.2_final.json` | Numerical gravitational wave spectrum data (JSON format) || `figure1.eps` | Main figure (EPS format, for publication) || `figure1.pdf` | Main figure (PDF format) || `figure1.png` | Main figure (PNG preview) || `README.md` | Overview and instructions || `CITATION.cff` | Citation metadata for software/research citation || `ABSTRACT.txt` | Plain text abstract | --- ## Reproducibility All code and data are publicly available to ensure full reproducibility: - **Zenodo archive:** https://doi.org/10.5281/zenodo.20198997- **Interactive visualization:** https://alikgimranov.github.io/ICC_GW/ --- ## Citation If you use this work in your research, please cite as: ```bibtex@misc{Gimranov2026_ICC_v3.2, author = {Gimranov, Alik}, title = {ICC v3.2: Lattice-Validated Topological Index Fluctuations Predict a Detectable Stochastic Gravitational Wave Background}, year = {2026}, doi = {10.5281/zenodo.20198997}, version = {3.2}}