Non-Hermitian Causal Memory Generates Observable Temporal Correlations Invisible to Spectral Analysis

Abstract: We identify a new class of non-Hermitian causal processes that produce statistically significant temporal correlations invisible to conventional spectral methods. Using a generative model with a strictly causal memory kernel, we demonstrate that time-asymmetric stochastic processes naturally yield sharp transitions at characteristic scales that appear as localized structures in similarity space but leave no trace in power spectra. The model predicts an asymmetric transition profile with orientation-dependent asymmetry parameter $A(θ)=A_0\cos(θ+δ)$ and achieves quantitative agreement ($χ^2/\mathrm{dof}=0.50$, $p=0.86$) with high-precision counting experiments exhibiting $p<10^{-15}$ significance. These results establish a fundamental limitation of spectral analysis for non-Hermitian, non-stationary processes and provide experimentally testable signatures of causal memory in open quantum systems.