Universal Structural Echo in Gravitational Wave Residuals with Constant Livolsi L=0.25

This work presents a data-driven analysis of post-merger residual signals from binary black hole mergers detected by the LIGO–Virgo network. The study uses publicly available strain data released through the Gravitational Wave Open Science Center (GWOSC), covering the gravitational-wave catalogs GWTC-1, GWTC-2.1, GWTC-3 and GWTC-4.0. The analysis is performed directly on raw strain data using a model-independent signal-processing pipeline. For each event, the post-merger residual signal is extracted, whitened and analyzed through autocorrelation techniques. To compare events with different total masses, the residual signals are normalized using the natural black hole time scale TBH=GM/c3T_{BH}=GM/c^3TBH=GM/c3. The resulting dimensionless delay variable allows stacking of residual autocorrelations across multiple events. The stacked analysis reveals a dominant peak located at τ/TBH≈4\tau/T_{BH} \approx 4τ/TBH≈4, indicating the presence of a universal temporal scale in the residual signal. The stability of this structure is verified through independent robustness tests, including temporal dataset splitting across observing runs and large-scale bootstrap resampling with 10,000 iterations. The detected scale corresponds to the emergence of a dimensionless constant L=0.25L = 0.25L=0.25, defined through the relation τ/TBH=1/L\tau/T_{BH} = 1/Lτ/TBH=1/L. Secondary peaks appearing near integer multiples of the fundamental delay suggest a possible harmonic structure of the residual response. All analysis steps are reproducible using the Python pipeline provided together with the dataset, enabling independent verification of the results using open gravitational-wave data.