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

• URL: http://arxiv.org/abs/2509.10174v1
• Date: Fri, 12 Sep 2025 12:04:13 GMT
• Title: Statistical Quantum Mechanics of the Random Permutation Sorting System (RPSS): A Self-Stabilizing True Uniform RNG
• Authors: Randy Kuang,
• Abstract summary: We present the Random Permutation Sorting System (RPSS), a novel framework for true uniform randomness generation grounded in quantum mechanics.<n>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.<n>A practical implementation, QPP-RNG, demonstrates how intrinsic system jitter, arising from microarchitectural noise, memory latency, and scheduling dynamics, interacts with complexity to yield a compact, self-stabilizing entropy source.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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