2025MNRAS.542..170Q

The goal of this work is to estimate the Hubble constant $H_0$ through the time-delay cosmographic study of the quadruply lensed, variable quasi-stellar objects (QSO) SDSSJ1433+6007. We combine multifilter, archival Hubble Space Telescope data for lens modelling with a dedicated 3-yr long time-delay monitoring campaign using the 2.1 m Fraunhofer telescope at the Wendelstein Observatory. The lens modelling is performed with the public LENSTRONOMY PYTHON package individually for the infrared data, utilizing the higher resolution of the optical data to constrain image positions a priori. This approach revealed two luminous contaminants in one of the near-infrared exposures, which would bias the lensing potentials and cosmological inference if left unaccounted. After masking these contaminants, we repeated the modelling and combined the lens posteriors, obtaining a constraint on the Fermat potential with a statistical uncertainty of $2.6\, {{\rm per\ cent}}$. The g'-band Wendelstein light-curve data are reduced and then analysed using a free-knot spline fitting method implemented in the public PYTHON PYCS3 tools, accounting for microlensing correction. We obtain a precision of $6.5\, {{\rm per\ cent}}$ for the time delays between the QSO images. By combining the posteriors for the Fermat potential differences and time delays, and assuming a flat Lambda-cold dark matter cosmology, we infer a Hubble constant of $H_0=71.7^{+3.9}_{-3.6}\, {\rm{km}}\,{\mathrm{Mpc}^{-1}~\mathrm{s}^{-1}}$, achieving $5.3\, {{\rm per\ cent}}$ purely statistical uncertainty for this single system. Complementary observations and further study are required to address the systematic errors fully.