Observable-Horizon-Guided Design Principles for Dynamic Noise Spectroscopy

This work identifies an observable-horizon–based design principle for dynamic noise spectroscopy. The central idea is that measurement-window selection and probe-frequency placement are controlled by the weakest Fisher-geometric direction of the reduced inverse problem. The analysis derives a finite optimal measurement window from the competition between statistical gain and filter-response decay, giving T∗=Tc/(2γ−1)T^* = T_c/(2γ - 1)T∗=Tc/(2γ−1) when γ>1/2γ > 1/2γ>1/2. It also gives a frequency-design rule: dimensionless probe frequencies should avoid the singular sensitivity point ω=1ω=1ω=1 and span both signs of ln⁡ωln ω. Together, these results frame the observable horizon as a structural constraint linking temporal and frequency design in dynamic spectral inference.