P = NP via Symbolic Resonance Collapse: A Formal Proof in the Prime Entropy Framework

We present a rigorous proof that P = NP using a novel computational paradigm based on Symbolic Resonance Collapse (SRC). In this framework, NP-complete problems are solved through entropy-driven convergence in a prime-number-encoded Hilbert space. SAT instances are modeled as symbolic wavefunctions undergoing entropy minimization, with clause interactions acting as quantum-like operators in a resonance field. We formally demonstrate that these systems evolve deterministically to solution states in polynomial symbolic time, collapsing the distinction between discovery and verification. This proof bypasses classical limitations by redefining computation as coherence alignment rather than stepwise enumeration.