PC-WAVES: Fourier Duality of Memory & Prediction

Background: Traditional cognitive theories treat memory and prediction as distinct processes involving separate neural mechanisms. This dichotomy has led to fragmented understanding of temporal cognition and limited theoretical integration across cognitive domains. Objective: We present PC-WAVES, a novel theoretical framework that unifies memory and prediction as two boundary projections of a single spectral transfer function within the Principia Cognitia (PC) cognitive architecture. Methods: Using Fourier analysis and Wiener filtering theory, we formalize the wave duality hypothesis where memory (retention kernel) and prediction (prospection kernel) emerge from the same underlying spectral object H(ω) through causal/anti-causal windowing operations. Results: The theory generates four testable predictions: (1) mid-band accuracy deficits in long sequences, (2) energy-constrained spectral shifts affecting short-term recall preferentially, (3) consolidation-mediated pole sharpening, and (4) external artifact anchoring of low-frequency spectral components. We provide mathematical mappings between spectral parameters and measurable cognitive metrics including memory half-life (t₁/₂), prediction horizon (L_pred), and quality factors (Q). Conclusions: PC-WAVES offers a parsimonious account of temporal cognition that bridges memory research, predictive processing, and spectral analysis of neural dynamics. The framework provides concrete experimental protocols for validating the unified theory across biological and artificial cognitive systems.