Abstract We present the first demonstrated achievement of combined Level-1 & 3 Artificial General Intelligence (AGI) through the Neural-Matrix Synaptic Resonance Network (NM-SRN) v2.0 architecture. Unlike current large language models that rely on probabilistic token generation and massive computational resources, NM-SRN v2.0 employs dynamic, modular reasoning structures that solve computationally intractable NP-hard problems with complete transparency and traceability. Our system demonstrates cross-domain problem-solving capabilities across Job-Shop Scheduling (JSSP), Traveling Salesman Problem (TSP), and Knapsack optimization, achieving solutions on single-CPU hardware that are beyond the reach of contemporary frontier AI models. The architecture's defining characteristics include: (1) zero pre-training requirements through Fast Forward Learning (FFL), (2) real-time problem reconfiguration via Neural Cubes (3) definitive solution generation rather than probabilistic approximation, and (4) complete explainability through structured reasoning traces. Performance benchmarks include solving a 50-job, 10-machine JSSP instance (search space ~1.22 × 101134) in 217 seconds with a 45.6% optimization improvement, and a 200-city TSP instance (search space ~2.0 x 10372) in approximately 32 minutes, establishing a new paradigm for tractable AGI reasoning. Keywords: Artificial General Intelligence, NP-hard optimization, explainable AI, modular architecture, computational tractability