Operational Non-identifiability of Single-epoch Low-rank RFI Mitigation: Controlled Failure-mode Analysis and HERA Evidence

The rapid proliferation of low Earth orbit (LEO) satellite constellations has introduced a new class of radio frequency interference (RFI) that poses a fundamental challenge to modern radio astronomy. In particular, unintended electromagnetic radiation emitted by satellite electronics exhibits strong temporal variability and weak spectral regularity, limiting the effectiveness of conventional mitigation techniques that rely on long term averaging or multi epoch observations. In this work, we investigate the fundamental limits of low rank interference mitigation in the single epoch regime, where only a single time frequency snapshot is available. We formulate satellite induced interference as a structured but non stationary component superposed on astrophysical signals and thermal noise, and analyze the conditions under which low rank decomposition can successfully suppress interference while preserving underlying astronomical information. Through controlled simulations and empirical analysis, we demonstrate that aggressive rank truncation can lead to substantial signal distortion, particularly for diffuse or low signal to noise astrophysical features. We quantify this trade off using preservation and suppression metrics, and show that beyond a critical interference strength, low rank methods inevitably induce irreversible information loss. Our results clarify the operational boundaries of low rank approaches for next generation radio observations and highlight the need for interference aware, data driven mitigation strategies tailored to the single epoch regime.