Classical Search by Wave Resonance: √N Scaling from Coupled Oscillators Without Quantum Postulates

Classical coupled harmonic oscillators on a complete graph locate a marked node in time proportional to √N — the same scaling as Grover's quantum search algorithm. No quantum postulates are required. The power-law exponent b = 0.4950 (theory: 0.5000) holds over N = 4..512, with t/√N flat at 316–325 steps across all sizes. The mechanism is Rabi oscillation between two collective modes: the resonant oracle lowers the marked node's spring frequency, creating an energy gap g = K/√N that drives amplitude concentration in time π/g ∝ √N. Control experiments confirm that without the oracle, no concentration occurs. Grover speedup is a wave phenomenon.