SAT Solving via Spectral Resonance: A Path to P = NP

Given the Boolean Satisfiability Problem (SAT), the first NP-complete problem, we seek to resolve the P = NP conjecture. Traditional methods demand exponential time. We pro- pose a spectral resonance framework, using the Hilbert-Pólya Operator (HPO) with zeta zeros, enhanced by Dα smoothing and unsatisfiability detection, achieving O(k· n2) com- plexity up to n = 1000. This structural method detects satisfiability via spectral resonance, validated up to n = 1000, and offers a computational path toward resolving P = NP.