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\section{Cosmographic Accuracy}  In this appendix we show how time delay precision can be approximately related to precision in cosmological parameters. parameters, thereby justifying the challenge requirements in that context.  We do so by considering the emulation of a joint inference of $H_0$ given a sample of $N$ observed strong lenses, each providing (for simplicity) a single measured time delay $\Delta t_k$. This $k^{\rm th}$ measurement is encoded in a contribution to the joint likelihood, which when written as a function of all the independently-obtained data $\mathbf{\Delta t}$ is the probability distribution  \begin{equation}  {\rm Pr}(\mathbf{\Delta t}|H_0) = \prod_{k=1}^N {\rm Pr}(\mathbf{\Delta t_k}|H_0).  \label{eq:prodpdf}  \end{equation}  If we knew that the uncertainties on the measured time delays were normally distributed, we could write the (unnormalised) PDF for each datum as  \begin{equation}  {\rm Pr}(\Delta t_k|H_0) = \exp \left[ -\frac{(\Delta t_k - \alpha_k / H_0)}{2(\sigma_k^2 + \sigma_0^2)} \right].  \label{eq:gaussian}  \end{equation}  Here, we have used the general relation that the predicted time delay is inversely proportional to the Hubble constant. Indeed, for a simulated lens whose true time delay $\Delta t_k^*$ is known, we can see that $\alpha_k$ must be equal to the product $(\Delta t_k^* H_0^*)$, where $H_0^*$ is the true value of the Hubble constant (used in the simulation). $H_0$ is the parameter being inferred: how different it is from the true value is of great interest to us. The denominator of the exponent contains two terms, that express the combined uncertainty due to the time delay estimation, $\sigma_k$, but also the uncertainty in the lens model $\sigma_0$ that would have been used to predict the time delay.  In practice, the probability for the measured time delay given the light curve data will not be Gaussian. However, for simplicity we can still use Equation~\ref{eq:gaussian} as an approximation, by asking for measurements of time delays to be reported as $\Delta t_k \pm \sigma_k$, and then interpreting these two numbers as above.