This paper presents the empirical verification results of the Quantum Relativistic Engine (QRE) operating within the qre-orchestrator-base environment. We analyze structural complexity and computational performance across classical NP-hard problem instances. Our empirical verification suite demonstrates a brute-force execution time of 79.8202 seconds for the Traveling Salesperson Problem (TSP) at N=12, alongside an accelerated heuristic resolution of 0.0035 seconds for N=1000. Additionally, a dynamic value tracking of 9565 was achieved for the Knapsack problem. These experimental benchmarks provide algorithmic insights into deterministic processing boundaries and polynomial-time verification mechanisms in the context of the official Clay Mathematics Institute formulation. ---Author Credentials & Professional Background:The author holds the IBM Full Stack Software Developer Professional Certificate and the IBM RAG & Agentic AI Professional Certificate. Official academic transcript and badge verifications are publicly accessible via Pearson Credly: https://credly.com
Marcos Mora (Sun,) studied this question.