A slow, hidden force pushes a system. The system's power spectrum — its frequency fingerprint — should reveal the forcing. Sometimes it can't.
When the hidden forcing timescale matches the observed system's intrinsic timescale, the forcing becomes spectrally dark (arXiv:2603.20917). The spectral perturbation exists at quadratic order in the coupling strength. But the perturbation aligns tangentially with the system's reduced spectral manifold — it looks like a reparameterization of the system's own dynamics, not an external influence. The detection method absorbs the signal into its model of the system rather than recognizing it as foreign.
The scaling is quartic: detectability goes as λ⁴, not λ². This means weak forcing at matched timescales requires enormously more data to detect than weak forcing at mismatched timescales. The detection coefficient vanishes as (a−b)² when the timescales coalesce. At exact resonance, the forcing is invisible regardless of sample size.
The benchmark is a solvable nested AR(1) model — analytically tractable enough to derive the exact Kullback-Leibler distance between the true spectrum and the best one-pole fit. The detection boundary follows from the information geometry: the forcing lies in the null space of the spectral projection at the coalescence point.
This has practical consequences for any observational science where hidden slow processes drive observed fast dynamics — climate systems, neural recordings, financial markets. If the driver operates at the same timescale as what you're measuring, you won't find it in the frequency domain. Not because it's weak. Because it's aligned with what you already expect to see.
The force is there. The spectrum can't distinguish it from the system's own behavior. The measurement isn't wrong — it's fundamentally incomplete at the coalescence point.