RNG Lab: A Reproducible Framework for Validation and Stream Management of MRG32k3a-Based Monte Carlo Simulations

Reliable and reproducible random number generation is fundamental to Monte Carlo simulation, stochastic optimization, and large-scale scientific computing. This paper presents RNG Lab, a reproducible software framework for stream management, validation, benchmarking, and provenance tracking of MRG32k3a-based random number generators. Rather than proposing a new random number generator, RNG Lab integrates deterministic stream-safe seeding, automated statistical validation, reproducible benchmarking, machine-readable provenance logging, and publicly archived reproducibility assets into a unified framework for transparent and repeatable scientific computing. The framework provides a reusable C/C++ implementation supporting masterseed, stream, and subsequence management together with jump-ahead functionality. A lightweight metaheuristic optimization component is used to explore practical outputcombination and tempering configurations while preserving the canonical MRG32k3a recurrence. Automated validation is performed using TestU01 and PractRand, complemented by held-out configuration validation, cross-stream correlation analysis, and generator-only throughput benchmarking. Experimental results show that the proposed framework passes the TestU01 Crush and BigCrush batteries while remaining PractRand-clean for large testing budgets under ordinary seed configurations. The selected configuration generalizes successfully to previously unseen validation seeds, maintains negligible empirical cross-stream correlation, and achieves improved generation throughput while preserving strong empirical statistical quality. Three reproducible Monte Carlo application studies—stochastic estimation of π, two-dimensional Ising-model simulation, and high-dimensional Monte Carlo integration—demonstrate deterministic replay, statistically consistent simulation behavior, and practical applicability to scientific computing workflows. The complete source code, datasets, validation logs, benchmark results, and reproducibility artifacts are publicly archived to facilitate independent verification, reuse, and future extension.