Can complete randomness hide perfect order?

This paper introduces a unified mathematical framework linking continuous and discrete random sequences through their structural baselines. While random numbers from any continuous distribution maintain an invariant mean spacing of exactly three observations between successive local maxima, discrete state spaces introduce plateaus that break this absolute invariance. We derive general closed-form expressions for the probability and structural period of local maxima under arbitrary discrete probability distributions. We prove that as the number of discrete states approaches infinity, the discrete baseline converges perfectly to the continuous baseline of three. Finally, we demonstrate practical applications for this lightweight computational test, including real-time algorithmic auditing of pseudo-random number generators, financial market trend diagnostics, and signal processing constraints in structured communications.