Testing Lens Models of PLCK G165.7+67.0 Using Lensed SN H0pe

Supernova H0pe is a multiply-imaged Type Ia supernova (SN~Ia) and the second lensed SN to yield a measurement of the Hubble constant by the time-delay cosmography method, finding $H_0=75.4_{-5.5}^{+8.1}{\text{km s}}^{-1}{\text{Mpc}}^{-1}$ (Pascale et. al 2025). We investigate the seven lens modeling approaches used to derive $H_0$, assessing their agreement with $\mathrm{\Lambda }\text{CDM}$ constraints from SN~Ia surveys through a purely observational comparison. $\mathbf{\text{We}}\mathbf{\text{test}}\mathbf{\text{each}}\mathbf{\text{lens}}\mathbf{\text{model}}\mathbf{\text{by}}\mathbf{\text{combining}}\mathbf{\text{its}}\mathbf{\text{predicted}}\mathbf{\text{magnifications}}\mathbf{\text{with}}\mathbf{\text{the}}\mathbf{\text{observed}}\mathbf{\text{time}}\mathbf{\text{delays}}\mathbf{\text{to}}\mathbf{\text{reconstruct}}\mathbf{\text{the}}\mathbf{\text{intrinsic}}\mathbf{\text{SN}}\mathbf{\text{Ia}}\mathbf{\text{luminosity}}\mathbf{\text{and}}\mathbf{\text{corresponding}}\mathbf{\text{distance}}\mathbf{\text{modulus.}}$ While photometrically derived magnifications yield distance moduli in line with $\mathrm{\Lambda }\text{CDM}$ expectations, our comparison reveals that lens model predictions, even the most precise ones, $\mathbf{\text{consistently}}\mathbf{\text{overestimate}}\mathbf{\text{the}}\mathbf{\text{magnification,}}\mathbf{\text{with}}\mathbf{\text{an}}\mathbf{\text{offset}}>1\mathbf{\text{mag}}$. This known bias, already appreciated by modeling teams, is independently confirmed through our analysis and highlights the value of lensed SNe as a tool to test model accuracy. If unaccounted for, such magnification biases can propagate into uncertainties in derived cosmological parameters, including $H_0$, a critical challenge for precision cosmology using strongly lensed transients.