Determination of $H_{0}$ with a Photometric AGN Golden Sample derived from a joint SN Ia-QSO cosmological reconstruction
The current tension between early and late-Universe determinations of the Hubble constant motivates the development of independent high-redshift distance tracers. Quasars, as luminous active galactic nuclei - AGNs, provide a promising route through the empirical relation between their X-ray and ultraviolet luminosities.We construct a joint Type Ia supernova-quasar Hubble diagram and investigate whether a statistically selected quasar subsample can define a preliminary golden sample for future AGN standardization. We combine calibrated Type Ia supernovae with SDSS DR14 quasars and infer the cosmological parameters from the posterior distribution of a joint model. Posterior medians and credible intervals are obtained from the marginalized distributions. We further define redshift-dependent quasar pools from SDSS queries and select the most representative sources in each bin using a multivariate statistical-distance criterion based on redshift, optical magnitudes, and SDSS colors. The posterior analysis yields $H_0 = 71.76^{+1.67}_{-1.31}\,\mathrm{km\,s^{-1}\,Mpc^{-1}}$ and $\Omega_m = 0.294^{+0.014}_{-0.012}$. The statistically selected quasar candidates reproduce the reference Hubble diagram with small residual dispersion across multiple redshift intervals and remain broadly distributed across the SDSS angular footprint without evidence of strong artificial clustering induced by the selection procedure.