Empirical Analysis of Ordered Spacing Geometry in Pseudo-Random and Constrained Sequences

This paper presents a structural statistical analysis of pseudo-random number generators (PRNGs), cryptographically secure pseudo-random number generators (CSPRNGs), and standardized cryptographic structures (UUID4, HMAC-SHA256) mapped into a sorted coordinate space. Instead of traditional time-domain randomness evaluations, we investigate the geometric properties of ordered sequences through empirical spacing analysis and uniform order statistics. Utilizing a localized first-order Autoregressive (AR(1)) delta trend framework combined with Median Absolute Deviation (MAD) filtering, we characterize the bounded corridor constraints inherent to ordered uniform distributions. Our empirical findings demonstrate that the localized spatial localization success observed in high-entropy primitives like HMAC-SHA256 is an expected mathematical artifact of sorted uniform spacings rather than a cryptographic vulnerability. Furthermore, we expand the analysis of UUID4 sequences to demonstrate how deterministic structural bit-masks imposed by RFC 4122 introduce measurable geometric artifacts and piecewise step-function discontinuities within the ordered spatial distribution.