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 γₑff = 3. 9. The resulting spectrum ΩGW (f) = Ω₀ (f/f₀) ^5-γₑff is fully compatible with CMB-S4 constraints on effective neutrino degrees of freedom (ΔNₑff = 0. 05092 < 0. 06). ICC v3. 2 predicts strongly detectable signals across multiple observational bands: ΩGW = 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 || γₑff | 3. 9 | Spectral index || ⟨ν²⟩ | 3. 6 ± 0. 12 | Topological index fluctuations (NANOGrav calibrated) || ΔNₑff | 0. 05092 | Effective neutrino degrees of freedom (CMB-S4 compatible) | --- ## Predictions for Gravitational Wave Detectors | Detector | Frequency | ΩGW (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 ΩGW < 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 ΔNₑff < 0. 01 while the NANOGrav signal remains consistent with ⟨ν²⟩ = 3. 6. 4. **Spectral slope deviation: ** High-precision spectral index measurement yielding γₑff ∉ 3. 7, 4. 1, inconsistent with the f^1. 1 scaling derived from ⟨ν²⟩ fluctuations. --- ## File Contents | File | Description ||------|-------------|| `ICCᵥ3. 2ₘanuscript. pdf` | Full manuscript in PDF format || `manuscript. tex` | LaTeX source of the manuscript || `references. bib` | BibTeX bibliography || `ICCᵥ3. 2final. 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/ICCGW/ --- ## Citation If you use this work in your research, please cite as: ```bibtex@miscGimranov2026ICCᵥ3. 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}