influence on Δ R$_{80}$ and Δ y$_{80}$ , which only depend on the relative dose difference between the measurement with and without magnetic field. 

The influence of the LET dependence of the film response was assessed by applying a polynomial cor- rection function [19] to the depth-dose curves. Taking into account the film-, energy-, dose- and possible setup-dependence of this method, this correction is not directly transferrable to this study but serves as a measure to estimate the influence of this effect. Thus, we estimate the uncertainty caused by this effect to be as high as the difference in Δ R$_{80}$ and Δ y$_{80}$ between the corrected and uncorrected data. 

The setup was aligned using the in-room laser system, rulers and a spirit level. Systematic setup uncer- tainties are related to translational and rotational degrees of freedom. 

A rotation of the film dosimeter relative to the beam axis has a direct impact on the mesured peak deflection. The alignment of the axes of the beam and the laser positioning system was uncertain to within 0 . 1 $^{o}$. The consequence of this angle on Bragg peak retraction and deflection have been assessed by purposefully rotating the dose distribution by this angle. 

Rotation of the magnet relative to the laser and of the phantom relative to the magnet were assessed by repeating the setup and irradiation procedure. For this analysis, the beam trajectory was determined for each depth as the mean of the two lateral positions receiving 10 % of the maximum dose. As no systematic dependence on the beam energy was observed in the deviations between the two experiments, mean absolute deviations were used as an estimate for this uncertainty. Rotations of the film relative to the phantom are statistical and therefore already covered. 

Translational uncertainties in x -direction were considered to be negligible, as they mostly lead to un- certainties in the amount of air traversed. An exception to this is the uncertainty of the pin positions (see Supporting Appendix A.1), which was below 10 µ m and therefore negligible. Translational uncertainties in y -direction were suppressed by setting the mean of the y -coordinate of the trajectory in the first 10 pixels to zero. Proton beam deflection in the magnetic fringe field outside of the magnet assembly was considered negligible. 

Another factor of uncertainty was introduced by the initial spatial achromaticity of the beam, i.e. a y - z -dependent energy spectrum, caused by the beam line design. This resulted in a kink towards the end of the trajectory, which lead to an overestimation of the beam deflection. This effect was observed both with and without magnetic field. The kink is about 3 mm in x - and 0 . 2 mm in y -direction. 

Relevant sources of uncertainty are summarized and quantified in Supporting Table A.1. The total uncertainty was estimated as the square root of the quadratic sum of the individual contributions. 

