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"This paper introduces Axiom-1, a novel post-generation structural reliability framework designed to eliminate hallucinations and logical instability in large language models. By subjecting candidate outputs to a six-stage filtering mechanism and a continuous 12.8 Hz resonance pulse, the system enforces topological stability before output release. The work demonstrates a fundamental shift from stochastic generation to governed validation, presenting a viable path toward sovereign, reliable AI systems for high-stakes domains such as medicine, law, and national economic planning."