Recent advances in video generation have made AI-synthesized content increasingly difficult to distinguish from real footage. We propose a physics-based authentication signature that real cameras produce naturally, but that generative models cannot faithfully reproduce. Our approach exploits the Moiré effect: the interference fringes formed when a camera views a compact two-layer grating structure. We derive the Moiré motion invariant, showing that fringe phase and grating image displacement are linearly coupled by optical geometry, independent of viewing distance and grating structure. A verifier extracts both signals from video and tests their correlation. We validate the invariant on both real-captured and AI-generated videos from multiple state-of-the-art generators, and find that real and AI-generated videos produce significantly different correlation signatures, suggesting a robust means of differentiating them. Our work demonstrates that deterministic optical phenomena can serve as physically grounded, verifiable signatures against AI-generated video.