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The rapid progress of text-to-image models has made AI-generated images increasingly realistic, posing significant challenges for accurate detection of generated content. While training-based detectors often suffer from limited generalization to unseen images, training-free approaches offer better robustness, yet struggle to capture subtle discrepancies between real and synthetic images. In this work, we propose a training-free AI-generated image detection method that measures representation sensitivity to structured frequency perturbations, enabling detection of minute manipulations. The proposed method is computationally lightweight, as perturbation generation requires only a single Fourier transform for an input image. As a result, it achieves one to two orders of magnitude faster inference than most training-free this http URL experiments on challenging benchmarks demonstrate the efficacy of our method over state-of-the-art (SoTA). In particular, on OpenFake benchmark, our method improves AUC by nearly $10\%$ compared to SoTA, while maintaining substantially lower computational cost.