tokens: Liao et al. 2015 ; Bonvin et al. 2017 ). Similarly, the ongoing public time-delay lens-modelling challenge (TDLMC; Ding et al. 2018 ) aims to test the accuracy of lens imaging modelling algorithms based on different source reconstruction techniques (e.g. Warren Dye 2003 ; Koopmans 2005 ; Vegetti Koopmans 2009 ; Oguri 2010 ; Birrer, Amara Refregier 2015 ; Nightingale Dye 2015 ). Additionally, the TDLMC may shed light on how critical the mass-sheet transformation (MST), a special case of source-position transformation, is (Falco, Gorenstein Shapiro 1985 ; Schneider Sluse 2013 , 2014 ; Xu et al. 2016 ; Birrer et al. 2017 ). All in all, the goal of the TDLMC is to understand how well we can control the systematic effects on σ κ . In addition, Birrer et al. ( 2015 ) used mock data to study whether we can use lens imaging to detect small perturbations on σ κ , while Chen et al. ( 2016 ) used mock data to study the impact of the unstable point spread function on σ κ when using adaptive optics imaging to study H 0 . However, it is difficult for mock data set challenges to reveal the systematics caused by unknown physical phenomena because the mock data only include known processes. The second method to assess systematic effects is to study physical processes that have not been previously considered. For example, Tie Kochanek ( 2018 ; hereafter TK18 ) have questioned the use of measured time delays in cosmography, by showing that, under the assumption of the ‘lamp-post’ model for accretion discs and differential magnification of the disc stars in the lensing galaxy (i.e. microlensing; Wambsganss 2006 ), the measured time delays may introduce a bias in the inferred value of H 0 . Under this assumed disc model, regions of the accretion disc that are separated by distances of the order of of light days vary in a coherent manner in response to activity in the centre of the disc. Differential magnification of portions of such a disc can introduce a phase delay due to the distance from the centre of the disc, and can shift the time-delay light curves by up to days depending on the accretion disk configuration and the microlensing pattern (see more description in Section 2 ). Since each lensed image has a different microlensing pattern, the sum of this proposed microlensing time-delay effect for any pair of lensed images can be non-zero. Therefore, the time delays we measure are not only the cosmological time delays but a combination of cosmological time delays and microlensing time delays, This effect, under certain assumptions, can significantly broaden the uncertainty on time-delay measurements, since it is embedded in the time-delay light curves (see fig. 10 in TK18 ). Although long-term monitoring can partially average out and mitigate this microlensing effect on time delays, the non-zero mean cannot be removed (see table 2 in TK18 ). Thus, TK18 have claimed that the current uncertainty of H 0 measurements from TDSL could potentially be underestimated
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