Context. Accurate X-ray spectroscopic measurements are fundamental for deriving basic physical parameters of the most abundant baryon components in the Universe. The plethora of X-ray observatories currently operational enables a panchromatic view of the high-energy emission of celestial sources. However, uncertainties in the energy-dependent calibration of the instrument transfer functions (e.g. the effective area, energy redistribution, or gain) can limit – and historically, did limit – the accuracy of X-ray spectroscopic measurements. Aims. We revised the status of the cross-calibration among the scientific payload on board four operation missions: Chandra, NuSTAR, XMM-Newton, and the recently launched XRISM. XRISM carries the micro-calorimeter Resolve, which yields the best energy resolution at energies ≥2 keV. For this purpose, we used the data from a 10-day-long observational campaign targeting the nearby active galactic nucleus NGC 3783, carried out in July 2024. Methods. We present a novel model-independent method for assessing the cross-calibration status that is based on a multi-node spline of the spectra with the highest-resolving power (XRISM/Resolve in our campaign). We also estimated the impact of the intrinsic variability of NGC 3783 on the cross-calibration status due to the different time coverages of participating observatories and performed an empirical reassessment of the Resolve throughput at low energies. Results. Based on this analysis, we derived a set of energy-dependent correction factors of the observed responses, enabling a statistically robust analysis of the whole spectral dataset. They will be employed in subsequent papers describing the astrophysical results of the campaign.
