Period-Finding by Resonance: Classical Coupled Oscillators Achieve √r Scaling Without Quantum Postulates

The quantum core of Shor's factoring algorithm — finding the period r of a^x mod N — is reproduced by classical coupled harmonic oscillators with no quantum postulates. The power-law exponent b = 0.4952 (theory: 0.5000) holds over r = 72..600 with t/√r flat at 293 ± 7 steps (coefficient of variation 2.5%), confirmed across 10 independent trials per case. Integer factoring follows directly: 15 semiprime cases, all factor pairs correct. The mechanism is Rabi oscillation between two collective modes at resonance: the period-marking oracle creates a detuning δΩ = K(r−2)/r, the mode coupling is g = K√((r−1)/r²) ≈ K/√r, and t_peak = π/g ∝ √r. Derived from Newton's equations. No wavefunction. No superposition axiom. No measurement collapse. Period-finding is a wave phenomenon.