The rapid advancement of Large Language Models (LLMs) makes it increasingly difficult to distinguish human writing from machine-generated text. Training-free detection offers a scalable solution, yet common confidence-based metrics mainly measure average token probabilities and often miss the signal fluctuations that characterize human writing, which we call "generative vitality". Spectral analysis offers a way to capture this vitality, but its mechanism and practical boundaries remain underexplored. In this paper, we analyze spectral detection from both theoretical and empirical perspectives. We connect spectral energy to variance in proxy log-probability trajectories and explain how broader human token choices create the fluctuations used by frequency-domain indicators. We further show that the strength of this signal depends on text length and sampling range: spectral evidence is clearest for long, continuous, constrained generation, while short, fragmented, mixed, and edited settings require complementary confidence and fluctuation views. These findings clarify when frequency-domain detection works and provide guidance for future multi-dimensional detector design.

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