Forensic Characterization of Correlated Residuals in Large Spectroscopic Pipelines: A Case Study of SDSS/BOSS Data

Large spectroscopic surveys rely on data reduction pipelines designed to remove instrumental signatures and deliver statistically well-behaved residuals. In this work, we perform a forensic statistical analysis of SDSS/BOSS optical spectra to explicitly test the assumption that these residuals behave as independent noise. Working in the observed frame and without applying redshift corrections, we construct residual spectra by subtracting a robust ensemble template and applying global power-spectral-density-based whitening. Despite the removal of dominant autocorrelations, we detect persistent, statistically significant correlation structures across spectra. Our results demonstrate that whitened spectroscopic residuals are not strictly independent, a finding with direct implications for uncertainty estimation and stacking-based analyses in precision cosmology. Key Findings Non-trivial structure: Detection of coherent subgroups in correlation space and stable low-dimensional embeddings. Robustness: The detected correlations survive aggressive null tests, including phase randomization, block shuffling, and bootstrap resampling. Invariance: Structure remains under wavelength reversal and multiscale Fourier decompositions, confirming it is not tied to specific astrophysical spectral features. Interpretation: The results point to residual instrumental or pipeline-induced correlations, rather than physical signal. Reproducibility This repository provides the complete pipeline to reproduce the diagnostic framework described in the paper. Download SDSS/BOSS spectra (FITS format) from SDSS SAS. Place the spectra in the data/ directory. Run the pipeline: python run_pipeline_paper.py (See data/README.md for specific formatting requirements.) Related work This release is part of a broader set of methodologically related reproducible analyses focused on structured residuals, residual covariance, localized correlation structure, and low-dimensional structure in astronomical data products. Related Zenodo records: Wavelength-Dependent Residual Correlations in JWST/MIRI LRS Time-Series SpectraDOI: 10.5281/zenodo.2034050 A reproducible analysis of structured residuals in James Webb Space Telescope NIRSpec dataDOI: 10.5281/zenodo.1957691 Forensic Characterization of Correlated Residuals in Large Spectroscopic Pipelines: A Case Study of SDSS/BOSS DataDOI: 10.5281/zenodo.20351879 Modular structure and low effective dimensionality in Euclid morphological data: a fully reproducible analysisDOI: 10.5281/zenodo.1965250 Together, these studies support a common methodological theme: high-dimensional astronomical data products can contain structured, localized, or modular residual covariance that may not be captured by global diagnostics alone.