Phase-Mediated Attractor Dynamics (PMAD) Reveals Structure in RXTE GRS 1915+105 Noise

This paper presents a phase-space, non-autonomous operator-theoretic reconstruction of the background noise sector in the black hole X-ray binary GRS 1915+105 utilizing Phase-Mediated Attractor Dynamics (PMAD). By applying a phenomenological state filter to eliminate macroscopic variability classes, I isolate and concatenate quiescent, non-QPO background noise intervals from 49 archival RXTE light curves. To decouple systemic pipeline constraints from active physical structure, the framework is subjected to a dual-null surrogate evaluation over the full 0–12 manifold spectrum. A pooled $\chi^2$ goodness-of-fit test strongly rejects an unstructured 1D raw timeline noise baseline ($\chi^2 = 58.8595, p = 1.65 \times 10^{-13}$), but uncovers a statistically flawless match with a 4D multivariate linear surrogate ($\chi^2 = 2.8583, p = 0.4140$). This establishes that the apparent low-dimensional geometric container—stabilizing at a modal peak of exactly 6 stiff axes for 42.86\% of the population—is an emergent property conditioned on the collinearity of the 12-dimensional embedding architecture. Crucially, to control for Type-I error inflation across the array, uncorrected parametric p-values were subjected to an array-wide Benjamini-Hochberg False Discovery Rate (FDR) correction ($\alpha=0.05$). Under this multi-test control, the pipeline successfully isolates a distinct, verified cohort of six independent segments ($N=6$, including d135, d157, d168, d185, d201, and d303) that aggressively reject the linear null hypothesis ($q < 0.05$). Shuffling the chronological sequence of these verified targets triggers immediate, explosive local trajectory divergence against the multi-channel covariance baseline, driven by authentic general relativistic phase-locking in the strong-field accretion flow. Within these localized pathways, continuous spectral trace evaluations confirm ultra-low-dimensional fractal manifold stabilization ($D_A \approx 0.16-0.34$). These results establish the PMAD architecture as a high-fidelity topological screening engine capable of filtering systemic windowing constraints to extract authentic, non-linear physical dynamics hidden within complex astrophysical time series.