SIMBAD references

We present a comprehensive test of the cosmic distance duality relation (DDR) using a combination of strong gravitational lensing (SGL) time delay measurements and Type Ia supernovae (SNe Ia) data. We investigate three different parameterizations of potential DDR violations. To bridge the gap between SGL and SNe Ia data sets, we implement an artificial neural network approach to reconstruct the distance modulus of SNe Ia. Our analysis uniquely considers both scenarios where the absolute magnitude of SNe Ia (M_B) is treated as a free parameter and where it is fixed to a Cepheid-calibrated value. Using a sample of six SGL systems and the Pantheon+ SNe Ia data set, we find no statistically significant evidence for DDR violations across all parameterizations. The consistency of our findings across different parameterizations not only reinforces confidence in the standard DDR but also demonstrates the robustness of our analytical approach.