Interface-Dependent Detectability in Astronomical Imaging: A Minimal Multi-Scale Stress Test Using Flux, Gradient, and Wavelet Operators

This technical note presents a minimal computational stress test showing that detectability in astronomical imaging depends not only on the injected signal, but also on the observational operator used to interrogate the data. A synthetic diffuse signal is injected into a real astronomical imaging background and analyzed through three distinct operators: flux-based smoothing, gradient-based detection, and wavelet-like scale-selective filtering. Detectability is evaluated across multiple injected signal scales and multiple template scales, producing explicit detectability maps in the two-dimensional space of signal scale versus template scale. The purpose of the note is strictly diagnostic and local in scope. It does not introduce new physical entities, new dynamics, or a general theory of observability. Instead, it isolates a reproducible methodological fact: the same underlying injected structure can be strongly detectable under one operator, moderately detectable under another, and remain sub-threshold under a third. The stress test shows in particular that flux-based operators recover diffuse structures with moderate robustness across a relatively broad range of scales, wavelet-like operators can outperform flux-based operators in scale-matched regimes, and gradient-based operators remain sub-threshold across the tested scale-space and do not provide competitive recovery for the injected diffuse signal. The resulting detectability maps make explicit that observability is operator-dependent and scale-dependent, even in a highly controlled setting with fixed data and fixed injected signal family. This record should therefore be read as a methodological clarification for inverse problems and detection pipelines in astronomical imaging. The note is intentionally narrow. It does not attempt to generalize beyond the computational construction presented, and it does not infer broader foundational conclusions from the toy model alone. This positioning is consistent with the diagnostic, local, and non-overclaiming publication strategy defined in your control protocol.