Statistical Quantum Mechanics of the Random Permutation Sorting System (RPSS): A Self-Stabilizing True Uniform RNG

We present the Random Permutation Sorting System (RPSS), a novel framework for true uniform randomness generation grounded in statistical quantum mechanics. RPSS is built on a pair of conjugate observables, the permutation count and the elapsed sorting time, whose heavy-tailed raw distributions synchronously converge to uniformity through modular reduction. This mathematically proven convergence establishes RPSS as a True Uniform Random Number Generator (TURNG). A practical implementation, QPP-RNG, demonstrates how intrinsic system jitter, arising from microarchitectural noise, memory latency, and scheduling dynamics, interacts with combinatorial complexity to yield a compact, self-stabilizing entropy source. Empirical validation under the NIST SP 800-90B framework confirms rapid entropy convergence and statistically uniform outputs. RPSS thus defines a new class of quantum-inspired entropy engines, where randomness is simultaneously harvested from unpredictable system jitter and amplified by combinatorial processes, offering a robust, platform-independent alternative to conventional entropy sources.

💡 Research Summary

The paper introduces the Random Permutation Sorting System (RPSS), a novel software‑defined framework for generating true uniform random numbers. RPSS is built around two conjugate‑like observables: the permutation count (ˆNₚ), i.e., the number of random permutation attempts required to recover an inverse permutation, and the elapsed sorting time (ˆT), i.e., the wall‑clock time taken for the whole sorting cycle. Because the underlying computing substrate (CPU pipelines, caches, memory latency, OS scheduling) exhibits stochastic jitter, the two observables cannot be simultaneously known with arbitrary precision; mathematically this is expressed as a non‑commuting relation