The presence of multiple orders in strongly correlated electronic materials like the cuprate superconductors, coupled with spatial inhomogeneity, poses a challenge to the interpretation of spectroscopic data taken on them. Here, we present a technique that directly acknowledges these orders and inhomogeneities and extracts statistically significant features from such data. Applying this technique to scanning tunneling spectroscopy measurements from single and bilayer cuprates spanning a wide doping range, we peer through local inhomogeneities and identify a gaplike feature that breaks translational and rotational symmetries and varies periodically in a fourfold pattern. This identification of spectral features aligns well with theoretical predictions of spatially modulated pair density. Published by the American Physical Society 2024