Simulation results. For a family of mock power laws with varying photon indices (centered at 2), redshift, Galactic absorption, exposure time, background, and response (all taken from real values), Xstack produces the stacked spectrum (assuming our data-driven response weighting factors) as yellow dots (“CTS/RSP”), resembling the input median power law well. For comparison, we present the stacked spectrum without Galactic absorption correction (green dots, “CTS/RSP,GalNH-uncorr”), and the stacked spectrum taking exposure as response weighting factors (red dots, “EXPO”). They both reproduce much more biased spectral shapes.