Detector-Invariant Informational Structure in Late-Time Gravitational-Wave Data: A Falsification-Driven State-Space Analysis

Detector-Invariant Informational Structure in Late-Time Gravitational-Wave Data: A Falsification-Driven State-Space Analysis Ankur Bhasin Bhasin Research Unit for Hyperphysics (BRUH) (Dated: December 22, 2025) Late-time gravitational-wave data provide a challenging regime for analysis, where signal-to-noise ratios are low and residual structure may be subtle, intermittent, and event-dependent. While ensemble-level studies have suggested the presence of coherence–information organization in latetime windows, the robustness of such structure under strict falsification tests remains unclear. In this work, we introduce a detector-invariant state-space framework to assess whether late-time gravitational-wave signals exhibit event-locked informational structure that survives adversarial validation. Using a shared phase-space representation built from robust envelope and df/dt observables, we construct empirical state-transition models and derive event-level metrics characterizing entropy, mixing, and effective attractor geometry. We subject this framework to a sequence of increasingly stringent falsification tests, including leave-one-event-out pairing, detector-rank consistency, run-conditioned controls, and a decisive offevent (noise-only) analysis using identical processing. We find that noise-only windows show no detector coupling and no fixed-point behavior, while on-event windows exhibit statistically significant cross-detector coupling in attractor-related metrics under a global-edge construction. These results demonstrate the presence of a weak but real detector-independent informational structure that is activated only during gravitational-wave events. The structure is not distributioninvariant, not rank-invariant, and not detectorspecific, consistent with a shared latent process viewed through differing projections. Our findings emphasize the importance of falsification-first analysis in late-time gravitational-wave studies and motivate future population-level investigations. I. INTRODUCTION Gravitational-wave observations have enabled detailed tests of strong-field gravity through inspiral, merger, and ringdown signals. Beyond the primary ringdown, latetime data remain comparatively underexplored due to low signal-to-noise ratios, nonstationary noise, and sensitivity to analysis choices. Several studies have proposed that late-time gravitational-wave signals may contain additional structure beyond simple damped oscillations, including echo-like features or relaxation phenomena. However, the statistical robustness and physical interpretation of such claims remain controversial, in part because late-time analyses are particularly vulnerable to pipeline artefacts, detector-specific effects, and a posteriori selection. Recent work across multiple physical domains has suggested that coherence–information organization may emerge statistically at the ensemble level, even when individual realizations are weak or unstable. This raises a critical question for gravitational-wave data: does any detector-independent informational structure exist at the level of individual events, and if so, does it survive strict falsification? The present work addresses this question using a deliberately conservative approach. Rather than testing for specific signal morphologies or templates, we ask whether late-time gravitational-wave data induce a shared lowentropy geometry in an empirical state space, detectable across instruments and absent in noise-only windows. Our focus is not detection significance, but robustness. II. DATA AND PREPROCESSING We analyze publicly available strain data from the Gravitational Wave Open Science Center (GWOSC) for binary black-hole events observed during LIGO–Virgo observing runs O1–O3. For each event and detector (H1, L1, and when available V1), strain time series are downloaded at a sampling rate of 4096 Hz and processed using consistent conditioning. Strain data are whitened, band-limited, and aligned such that t= 0 corresponds to the reported merger time. We focus on late-time windows following the primary signal, excluding the peak merger region. To construct falsification controls, we also analyze offevent windows drawn from the same strain data at times well separated from the merger, using identical preprocessing, windowing, and analysis parameters. III. STATE-SPACE CONSTRUCTION A. Windowed observables Late-time data are partitioned into overlapping analysis windows. For each window we compute two robust observables: 1. a logarithmic envelope-based coherence proxy derived from the analytic signal, 2. a robust df/dt proxy characterizing the local rate of change of the envelope. 2 These observables are chosen for numerical stability and interpretability. No physical model is assumed. B. Shared phase-space representation Each window is mapped into a two-dimensional phase space spanned by the coherence proxy and the df/dt proxy. The phase space is discretized into a fixed grid, yielding a finite state representation. Two discretization strategies are considered: •Global edges (Option A): a single shared binning trained on all signal-containing windows. •Run-conditioned edges (Option B): separate binning for each observing run, with a global fallback for sparsely populated cases. The global-edge construction provides maximal comparability across detectors, while the run-conditioned construction controls for potential calibration drift. C. Empirical transition models Within each event and detector, the sequence of visited states defines an empirical state-transition matrix. These matrices are used solely as compact summaries of statespace traversal. The Markov representation is not interpreted as a physical dynamical model. All conclusions are based on comparative invariance and falsification tests rather than on the literal validity of a Markov assumption. IV. EVENT-LEVEL METRICS From each empirical transition matrix we compute a set of summary metrics, including: •entropy rate, •spectral gap, •stationary distribution entropy, •an effective attractor strength, defined as the dominance of the leading low-entropy basin in the stationary distribution. The term effective attractor refers to a dominant lowentropy basin in the empirical state space and does not imply deterministic dynamics. V. FALSIFICATION FRAMEWORK Event-level metrics are paired across detectors for the same gravitational-wave event. Statistical significance is FIG. 1. Event-wise detector pairing for effective attractor strength using a shared global state space. Each point corresponds to a single gravitational-wave event, paired across H1 and L1 detectors. Blue points indicate on-event late-time windows, while orange points show off-event noise-only windows processed with identical binning and analysis. A positive correlation is observed only for on-event data, while noise-only windows show no detector coupling. assessed using permutation tests that randomize detector pairings. Rank invariance and marginal distribution equality are explicitly tested and expected to fail, consistent with differing detector projections of a shared latent structure. As a decisive falsification, the entire pipeline is applied to off-event noise windows using the same global state space. Any detector coupling observed in noise would invalidate the on-event results. VI. RESULTS Noise-only windows show no detector coupling across all tested metrics. Correlations are consistent with zero under permutation testing, and no fixed-point or attractor structure is observed. This rules out binning artefacts, Markov construction artefacts, and detectorspecific noise as explanations for the on-event behavior. Using a shared global state space, on-event windows exhibit statistically significant cross-detector coupling in attractor-related metrics. Effective attractor strength shows robust event-wise correlation across detectors, while entropy rate and mixing metrics are weaker or absent. Marginal distributions and rank orderings differ across detectors, as expected. When run-conditioned edges are used, detector coupling weakens but does not invert or appear in noise-only windows. This behavior is consistent with partial smearing due to run-specific calibration effects and supports the interpretation of a real but weak shared structure. 3 FIG. 2. Permutation null test for detector coupling in effective attractor strength (H1 vs L1). Histograms show the null distributions obtained by randomizing detector pairings for on-event data (blue) and noise-only windows (orange). Vertical lines indicate the observed correlation coefficients. A statistically significant deviation from the null is present only for on-event data, while noise-only windows are fully consistent with the null hypothesis. VII. DISCUSSION Our results demonstrate the existence of a detectorindependent informational structure in late-time gravitational-wave data that is activated only during gravitational-wave events and absent in noise-only windows. The structure is weak, event-dependent, and neither distribution-invariant nor rank-invariant, consistent with a shared latent process viewed through differing detector projections. The use of a Markov representation changes numerical values of entropy-related quantities but does not introduce the observed detector-invariant structure, as demonstrated by its complete absence in noise-only windows processed with the identical state space. VIII. CONCLUSION We have presented a falsification-driven framework for analyzing late-time gravitationalwave data that emphasizes detector invariance, robustness, and noise rejection. Our findings indicate that gravitational-wave events induce a weak but real shared informational structure across detectors, while noise does not. ACKNOWLEDGMENTS The author thanks the LIGO–Virgo Collaboration for public data access via GWOSC. This work was conducted independently under the Bhasin Research Unit for Hyperphysics (BRUH). [1] R. Abbott et al. (LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration), SoftwareX 13, 100658 (2021). [2] V. Cardoso, E. Franzin, and P. Pani, Phys. Rev. Lett. 116, 171101 (2016). [3] J. Abedi, H. Dykaar, and H. Afshordi, Phys. Rev. D 96, 082004 (2017). [4] M. Maggiore, Gravitational Waves. Volume 2 (Oxford University Press, 2019).