I have been playing with a physics theory and extention of signal detection. When applied to ML the results have been wild. Instead of posing on arXiv first, the best proof I can have is the AI community tear into it and reproduce their own results and work. Have fun and welcome to my nightmare. Author: Douglas Kenworthy (Student) Template-Free Detection of Delay-Consistent Narrowband Coherence in Distributed Stochastic Sensor Networks Abstract Detecting weak causal coupling in distributed sensor networks is challenging when the underlying signal waveform, spectrum, and onset time are unknown and local signal-to-noise ratios are low. Standard correlation and coherence measures frequently exhibit spurious narrowband structure under independence, particularly in long-duration or colored-noise data, limiting their utility for causal inference. I introduce a template-free method for detecting statistically significant narrowband coherence conditioned on physically admissible time-delay constraints between spatially separated sensors. The method assumes only wide-sense stationarity under the null hypothesis of independence and does not require signal templates, parametric models, or training data. Causal coupling is treated as a constraint-satisfaction problem in the joint time–frequency domain, where coherence must persist across frequency bins and satisfy bounded delay consistency. I derived conservative bounds on false detections under independence and show that enforcing delay consistency across multiple sensors rapidly suppresses spurious coherence events. The method is validated using publicly available interferometric time-series data, demonstrating recovery of weak, delay-consistent coherence features that are not detectable using standard broadband correlation or coherence thresholds alone. Introduction Distributed sensing systems are routinely deployed in regimes where signals of interest are weak, transient, or intentionally obscured by noise. In such environments, the form, spectrum, and timing of a potential common influence may be unknown, rendering matched filtering, parametric modeling, and learning-based approaches ineffective or brittle under novelty. Classical dependence measures such as cross-correlation and magnitude-squared coherence quantify statistical association but do not, by themselves, distinguish causal coupling from coincidental alignment in stochastic processes. In long-duration or colored-noise data, narrowband coherence peaks commonly arise under independence, complicating causal interpretation. This work addresses a narrower but logically prior question: does the data contain statistically significant evidence of a shared causal influence consistent with physical propagation constraints? We propose a template-free detection criterion based on narrowband coherence conditioned on admissible inter-sensor delays. By enforcing physical delay consistency across frequency bins and sensor pairs, the method strongly suppresses spurious detections while remaining agnostic to signal form. Problem Formulation Consider a set of spatially separated sensors indexed by observing real-valued time series x_i(t) = s_i(t) + n_i(t), The signal components may arise from a shared physical cause, but the waveform, spectrum, and onset time are unknown. The objective is not signal reconstruction, but detection of statistically significant causal coupling consistent with bounded propagation delays determined by sensor geometry. Delay-Consistent Narrowband Coherence 3.1 Time–Frequency Representation Each sensor time series is segmented into overlapping windows of duration , and a short-time Fourier transform (STFT) is computed: X_i(f, t). 3.2 Delay-Indexed Cross-Spectral Coherence For a candidate delay , define the delay-compensated cross-spectrum: S_ij}(f, \Delta) = \mathbb{E}t \left[ X_i(f,t),X_j^*(f,t+\Delta) \right], C{ij}(f,\Delta) = \frac{(f,\Delta)|^2} \mathbb{E}_tt|X_j(f,t+\Delta)|^2}. 3.3 Physical Delay Constraints Let us denote the physically admissible delay interval between sensors and , determined by their separation and an upper bound on propagation speed. Definition (Delay-Consistent Coherence) A sensor pair exhibits delay-consistent coherence at frequency if \exists,\Delta \in \mathcal{T}{ij} \text{ such that } C_{ij}(f,\Delta) > \gamma, Joint causal coherence across a sensor set requires the existence of delays such that all pairwise delays are mutually consistent. Statistical Properties Under Independence Under , narrowband coherence peaks arise with nonzero probability due to finite-sample effects and spectral leakage. However, the probability that such peaks simultaneously satisfy: spectral localization, bounded physical delays, persistence across frequency bins, consistency across multiple sensors, decays rapidly as constraints are added. Theorem 1 (False Detection Suppression) Under independence and wide-sense stationarity, the probability of observing joint delay-consistent narrowband coherence across sensors decays superlinearly with , assuming approximate independence across frequency bins. This result motivates treating causal detection as a constraint-satisfaction event rather than a threshold-crossing event. Empirical Validation Using Public Interferometric Data 5.1 Dataset Validation is performed using publicly available gravitational-wave interferometer strain data from the LIGO O1, O2, O3 observing runs and strain data. The Hanford and Livingston detectors provide geographically separated, low-SNR time series dominated by non-Gaussian noise. No astrophysical templates or event timing are used. All data and metadata are available through the LIGO Open Science Center. 5.2 Procedure Acquire strain data from both detectors. Apply aggressive downsampling and narrowband isolation. Compute delay-indexed coherence across admissible inter-site delays. Evaluate significance using time-shifted surrogate data. 5.3 Results Isolated coherence peaks appear frequently in surrogate data, confirming that coherence alone is insufficient for causal inference. When coherence is conditioned on admissible delays, false detections drop sharply. Persistent, delay-consistent narrowband features appear in unshifted data and disappear under time randomization. These features are not detectable using standard broadband correlation or coherence thresholds. Relation to Prior Work Cross-correlation and coherence quantify dependence but not causality. Generalized cross-correlation presumes a reconstructible signal. Granger causality relies on parametric prediction models. Learning-based approaches depend on priors and training data. The present method differs by inferring causality through violation of independence under physical delay constraints, without modeling, prediction, or learning. Discussion The results demonstrate that enforcing physical delay consistency transforms narrowband coherence from a noisy dependence measure into a robust causal detection primitive. The method is invariant to waveform shape and remains effective under extreme noise and novelty. While demonstrated on interferometric data, the framework applies broadly to distributed stochastic sensing systems where physical propagation constraints are known. Conclusion I have introduced a template-free, physics-grounded method for detecting weak causal coupling in distributed sensor networks. By conditioning narrowband coherence on admissible delays and multi-sensor consistency, the method suppresses spurious detections under independence while remaining agnostic to signal form. Validation using public interferometric data demonstrates recovery of weak causal structure in regimes where conventional methods fail. Data and Reproducibility All datasets used in this study are publicly available. The method requires no training data or templates. Implementation requires only time–frequency decomposition, delay-indexed coherence computation, and enforcement of physical delay constraints. References (Include standard references to coherence, GCC, Granger causality, and LIGO open data papers.) My hope is you can re produce the results that end with NO llm hallucination, but I am terrible at coding. Having experts in AI apply and re produce results will help me back up my physics work and might make surprising advancements. Physics student to Ai community. submitted by /u/WAR_Grisom
Originally posted by u/WAR_Grisom on r/ArtificialInteligence
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