Global Fractal Temporal Correlations in Gravitational-Wave Detector Noise: A Cross-Detector, Cross-Epoch, and Null-Model Study

# 📄 Global Fractal Temporal Correlations in Gravitational-Wave Detector Noise: A Cross-Detector, Cross-Epoch, and Null-Model Study **Preprint / Working Paper** > **👤 Author:** Krzysztof Żuchowski > **🏢 Affiliation:** Independent Researcher — Fractal Information Theory Project > **📅 Date:** 2026-01-04 > **🆔 Phase:** QW-1660 (Extended Audit) --- ## 📝 Abstract We report a systematic, multi-phase investigation of long-range temporal correlations in gravitational-wave interferometer strain data, using publicly available LIGO and Virgo open datasets. Across a sequence of increasingly stringent tests (QW-1660 v5–v24), we identify statistically significant fractal scaling behavior, characterized by nontrivial Hurst exponents, that is consistent across detectors, observational epochs, and analysis windows. Crucially, cross-detector correlations persist under phase-randomized surrogate tests that preserve the power spectral density, while disappearing under temporal shuffling. This demonstrates that the observed correlations cannot be attributed to shared spectral features, stationary Gaussian noise, or instrumental artifacts. Our results indicate the presence of a global, phase-robust, long-range temporal structure in the gravitational-wave strain background, extending beyond the assumptions of purely local noise models. While compatible with General Relativity at the level of local dynamics, these findings suggest that the statistical structure of spacetime fluctuations may possess a deeper, scale-invariant organization. --- ## 🔬 Key Empirical Findings This study presents three critical pieces of evidence rejecting the "Standard Gaussian Noise" hypothesis: ### 1. Cross-Epoch Stability (v21/v22) The fractal memory is stable across years of observation, independent of detector upgrades or environmental changes: * **Single-Detector range:** $H \approx 0.27 - 0.31$ (Consistent throughout O3 and Early O4) * **O4 Verification:** $H \approx 0.33$ (v22) ### 2. Cross-Detector Correlations (v24) Statistically significant phase-robust fractal correlations are detected between geographically separated interferometers using the correlation-based Cross-Hurst estimator: * **H1–L1 Correlation:** $H_{xy} = 0.361$ ($> 5\sigma$ significance) * **L1–V1 Correlation:** $H_{xy} = 0.270$ ($> 5\sigma$ significance) ### 3. Null-Model Validation (v19/v24) * **Time Shuffling:** Destroys the correlations ($H \to 0.5$), proving they are truly temporal/memory-based. * **Phase Randomization:** Preserves the correlations ($H \approx H_{real}$), proving they are **irreducible to the Power Spectral Density (PSD)** and represent genuine phase-robust structure. --- **Additional notes** **Relation to prior literature** Fractal and multifractal analysis techniques have previously been applied to gravitational-wave data, though primarily to transient signals or auxiliary channels rather than the background strain noise on a global scale. - Chernogor, L. F., Lazorenko, O. V., & Onishchenko, A. A. (2018). Multi-fractal analysis of the gravitational waves. *Journal of V. N. Karazin Kharkiv National University, Series Physics*. https://periodicals.karazin.ua/physics/article/view/10081 - Nepomuceno, M. M. F., de Freitas, D. B., & de Medeiros, J. R. (2018). On the multifractality in GW150914 gravitational wave. *Boletim da Sociedade Astronômica Brasileira*. https://sab-astro.org.br/wp-content/uploads/2018/10/MacksonNepomuceno.pdf de Freitas, D. B. et al. (2019). Multifractal signatures of gravitational waves detected by LIGO. arXiv:1912.12967 https://arxiv.org/abs/1912.12967 - Cavaglià, M. et al. (2022). Characterization of gravitational-wave detector noise with fractals. *Classical and Quantum Gravity* **39**, 135012. arXiv: https://arxiv.org/abs/2201.09984 Published: https://doi.org/10.1088/1361-6382/ac7325 - Longo, A., Bianchi, S. et al. (2020–2021). Local Hurst exponent computation on triaxial seismometer data for Virgo and KAGRA environmental monitoring. (e.g. Longo & Bianchi, *Pure and Applied Geophysics*, 2021) The present work significantly extends these earlier studies. While previous analyses focused on individual gravitational-wave events (such as GW150914) or local properties of auxiliary seismic channels, this study provides the **first global, cross-detector (H1–L1–V1), cross-epoch analysis of the background strain noise** from public O3 and early O4 data using Detrended Fluctuation Analysis (DFA) for Hurst and Cross-Hurst exponents, together with rigorous surrogate testing (phase randomization and time shuffling). The results reveal globally consistent, phase-robust, long-range temporal correlations (single-detector H ≈ 0.27–0.36; cross-detector H_xy ≈ 0.215–0.36) that survive phase randomization but collapse under time shuffling — a signature of persistent temporal memory not previously reported in the gravitational-wave detector noise literature. --- ## 📂 Associated Resources * **Preprint PDF:** `Global_Fractal_Correlations_in_GW_Noise_Preprint.pdf` * **Replication Code (Kaggle):** [Phase 16 - Raw Strain Fractal Audit](https://www.kaggle.com/code/krzysztofzuchowski/phase-16-raw-strain-qw-1660-v5-fractal) **RUN FIRST QW-1660 v2 !!!** Data required by v5-v24 scripts is retrieved via the *QW-1660 v2: HOLOGRAPHIC NOISE SEARCH* cell. * **Analysis Data:** `QW_1660_v24_cross_hurst_null_validation.json` * **Project Repository:** [GitHub](https://github.com/hyconiek/Fractal-Nadsoliton-Theory) --- **Keywords:** Gravitational waves, Hurst exponent, Fractal noise, Non-Markovian dynamics, LIGO, Virgo, Stochastic background.