Observed projected proper length PDFs for SDSS-classified quasar and non-quasar giants, obtained through kernel density estimation. We used a Gaussian kernel with σ_KDE = 75 kpc. For both panels, two-sample Kolmogorov–Smirnov tests yield p < 1‰. However, given the severe impact of selection effects, we could not reject the null hypothesis that quasar giants and non-quasar giants have the same underlying projected proper length distribution. Top: newly discovered (LoTSS DR2) giants with SDSS spectral class labels. Bottom: all known giants with SDSS spectral class labels.