The proposed Spatial Unfolding methodology transforms temporally recursive radix-4 digit-recurrence division into a fixed-depth spatial computation by replacing iterative execution with a cascade of identical combinational processing stages. As a result, deterministic single-cycle latency is achieved independently of operand values.

Accurate detection of P-wave arrival times is fundamental to earthquake localization, seismic monitoring, and early earthquake warning systems. Although deep learning approaches have recently demonstrated high performance in seismic phase picking, their dependence on large, labeled datasets, substantial computational requirements, and limited interpretability remain significant practical limitations. In this study, we propose a simple but effective method for automatic P-wave arrival detection based on entropy analysis of seismic signals in phase space. The proposed method represents seismic waveforms in a two-dimensional phase space constructed from the signal amplitude and its temporal derivative, enabling characterization of structural transitions associated with the onset of P-wave arrivals. The normalized information entropy ratio (IER) is computed from joint and conditional probability distributions within sliding time windows, and abrupt entropy transitions are used to identify arrival times. The method was evaluated using a globally compiled and filtered dataset of seismic events obtained from the EarthScope/IRIS data services, covering diverse seismic regions and recording conditions. A parameter sensitivity analysis was conducted for window size, discretization resolution, and entropy threshold. The proposed approach achieved a maximum P-wave detection recall of 94.4% under optimal parameter settings (ΔIER = 0.5, N = 5000, M = 70). These results demonstrate that phase-space entropy analysis is a promising and computationally efficient approach for automatic P-wave detection under the investigated experimental conditions.