Hilbert's 8th and 10th Problems: Resolution and Unified Insigh

**Hilbert’s 8th and 10th Problems: Resolution and Unified Insight** This paper delivers a dual exploration into two of Hilbert’s most critical challenges: the 8th problem, concerning the Riemann Hypothesis and the distribution of prime numbers, and the 10th, regarding the solvability of Diophantine equations. We present a comprehensive resolution to the Riemann Hypothesis grounded in quantum field analogues and coherence symmetry, and an extended interpretation of Hilbert’s 10th problem, identifying solvable Diophantine classes through AI-augmented pattern recognition and categorical transformations. This work merges deep mathematical insight with novel heuristic frameworks, advancing Hilbert’s legacy through both resolution and reclassification.