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

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 late-time 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 constructed from robust envelope-based and df/dt observables, we build empirical state-transition models and derive event-level metrics characterizing entropy, mixing, and effective attractor geometry.

The framework is subjected to a sequence of increasingly stringent falsification tests, including detector pairing, permutation testing, rank and distribution invariance checks, run-conditioned controls, and a decisive off-event (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.

The observed structure is weak, event-dependent, and not distribution-invariant, consistent with a shared latent informational process viewed through differing detector projections. These results demonstrate that late-time gravitational-wave events induce a real but fragile detector-independent informational structure, emphasizing the importance of falsification-first analysis in late-time gravitational-wave studies.