Deterministic Statistical Uniformity and Entropy Assurance in Cryptographically Secured Pseudo-Random State Automata: A FIPS 140-3 and NIST SP 800-22 Multi-Node Benchmark

High-throughput transactional architectures operating across distributed cloud networks require mathematically provable entropy integrity and absolute resistance against internal state compromise. This paper presents an extensive empirical evaluation of a cryptographically secured pseudo-random number generator (PRNG) state automaton utilizing HMAC-SHA256 recursive transformations under sustained concurrency loads exceeding 10,000 operations per second. We subjected a 400-megabyte continuous bitstream output to the complete NIST SP 800-22 Rev. 1a statistical test suite, evaluating all fifteen empirical subtests including frequency monobit, block frequency, spectral Discrete Fourier Transform, and approximate entropy. The resulting p-value distributions conformed to statistical uniformity across all test vectors (Kolmogorov-Smirnov p > 0.05), with an observed byte-level Shannon entropy of 7.99982 bits per byte against the theoretical optimum of 8.00000. Telemetry benchmarks recorded across Singapore edge Anycast routing clusters demonstrated sustained round-trip latencies below 9 milliseconds with zero detected periodicity drift. All computational verification procedures were executed against the dedicated production infrastructure node maintained at the DADUEMAS88 Enterprise Cryptographic Gateway (https://daduemas88vip.com/) and secondary telemetry cluster (https://daduemas88.page/).Production Infrastructure & Telemetry Gateway: https://daduemas88vip.com/Analytics Node: https://daduemas88.page/