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

# 📄 Global Fractal Temporal Correlations in Gravitational-Wave Detector Noise: A Relational Functional Approach **Scientific Preprint / Working Paper (Release 4.4)** > **👤 Author:** Krzysztof Żuchowski > **🏢 Affiliation:** Independent Researcher — Fractal Information Theory Project > **📅 Date:** 2026-01-06 > **🆔 Phase:** QW-1660 (Complete Raw-Strain Audit v5–v46) --- ### ⚠️ Note on Document Versions (Reading Guide) This release comprises two distinct documents serving different scientific functions: * **📄 Version 3: Publication Manuscript** * *Title:* "Global Fractal Temporal Correlations in Gravitational-Wave Detector Noise" * **Purpose:** Designated for **peer review and journal submission**. This version presents the core empirical results and theoretical deductions in a streamlined format, adhering to standard publication constraints. * **Recommendation:** Reviewers and general readers should start here. * **📂 Release 4.4: Technical Audit & Theoretical Ledger** * *Title:* "Fractal Information Nadsoliton (FIN) as a Relational Correlation Functional" * **Purpose:** Serves as the **comprehensive evidence base**. It contains the full Phase 16 audit trail (v5–v46), detailed "Zero-Assumption" physical validation tests, and the complete raw-strain logs required for replication. * **Recommendation:** For use by researchers performing replication studies or verifying the complete rigorous history of the QW-1660 protocol. --- ## 📝 Abstract We report the final results of a systematic, multi-phase investigation of long-range temporal correlations in gravitational-wave interferometer strain data, encompassing the complete Phase 16 audit (v5–v46). Using publicly available LIGO and Virgo open datasets across O3 and O4 runs, we identify a robust, scale-invariant fractal signature characterized by a Hurst exponent $H_{\text{FIN}} \approx 0.23 \pm 0.02$. This investigation formally identifies the **Fractal Information Nadsoliton (FIN)** not as a local signal or stochastic process, but as a **Relational Correlation Functional** $\mathcal{F}_{\text{FIN}}$. Through extensive physical audits (v28–v46), we demonstrate that this functional transforms tensorially, is strictly non-energetic, and exhibits strong coupling to cosmic-time redshift proxies ($\rho \approx -0.96$). These findings provide empirical evidence for a phase-robust informational background in spacetime fluctuations, consistent with the FIN framework's predictions for a consistent UV-completion of gravity. --- ## 🔬 Key Empirical Breakthroughs (Release 4.4) This release establishes the final empirical ledger for the FIN functional across three critical dimensions: ### 1. The Relational Axiom (v25--v46) FIN is formally defined as a relational measure between fields, irreducible to single-channel Gaussian noise: * **Universality:** Identified with the **log-Poisson cascade** universality class (typical of quantum vacuum and CMB noise). * **Identity:** The empirical $H \approx 0.23$ yields a fractal dimension $D = 1.77$, matching the theoretical Nadsoliton network density $N(d) \sim d^{1.77}$. ### 2. Comprehensive Physical Audit (v28--v46) A rigorous battery of "Zero-Assumption" tests established the physical nature of FIN: * **Scale Invariance (v36, v45):** $dH/d\log L \approx 0$; the signature is independent of detector geography and arm length. * **Tensoriality (v37, v44):** $\Delta H_{+,\times} > 0.1$; the functional follows metric-mode transformation laws. * **Energy Independence (v39, v45):** $\rho(H, E_{\text{RMS}}) \approx 0$; FIN carries structure without energy transport. * **Cosmic Coupling (v40--v41):** $\rho(H, z) \approx -0.96$; strong correlation with redshift and GW event rates. ### 3. Structural Stationarity (v43) Moving-window analysis confirms that FIN is a **structural measure of reality**, not a dynamic process: * **Stability:** $\sigma(H) \approx 7 \times 10^{-4} \ll 0.02$. --- **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 * **Primary Manuscript (Version 3):** `Global_Fractal_Correlations_in_GW_Noise_Preprint.pdf` * *Status:* **Recommended for Reading/Review.** Streamlined for clarity and publication standards. * **Technical Ledger (Version 4):** `Global_Fractal_Correlations_in_GW_Noise_Preprint_Release_4_4.pdf` * *Status:* Complete empirical history including Phase 16 (v5–v46) raw strain audits. * **Archive Documentation:** `TOE_FINAL_DOCUMENTATION 4.4.pdf` * **Replication (v5-v24):** [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 the scripts is retrieved via the *QW-1660 v2: HOLOGRAPHIC NOISE SEARCH* cell. * **Replication (v25-v46):** [Full Fractal Signature](https://www.kaggle.com/code/krzysztofzuchowski/full-fractal-signature) * **Project Repository:** [GitHub](https://github.com/hyconiek/Fractal-Nadsoliton-Theory) --- **Keywords:** Gravitational waves, Relational Functional, Hurst exponent, Fractal Information Nadsoliton, Log-Poisson cascade, Spacetime Information.