Type	Uncertainty Source $\left({\alpha }_i\right)$ and Symbol	Source of assumed value	Evaluation of $\text{k}=1{\sigma }_{{\alpha }_i}$	Evaluation of $\left(\frac{\partial SPR}{\partial {\alpha }_i}\right)$
A	Curve Fit Error	The depth of maximum relative ionization of each sample is assumed to be uniformly distributed between the minimum and maximum ranges predicted by the three different curve-fit models. Therefore, the assumed value is the average of the maximum and minimum proton beam ranges estimated using 3 different curve fit methods.	Following the uniform distribution assumption, ${\sigma }_{{\alpha }_i}$ will then be the standard deviation of the uniform distribution characterized by the maximum and minimum estimated ranges from the three different curve fit models. $\left[{\text{R}}_{\min },{\text{R}}_{\max }\right]$	Analytical derivatives of Eq. (1) for ${\alpha }_i$ and ${\sigma }_{{\alpha }_i}$ for each substance considered in each Geant4 physics list simulation.
A	Detector Noise	Derived from dose fluctuations in simulations.	${\sigma }_{noise}$ = root mean square differences between boxcar-filtered and original depth-ionization curves.	Add 1% and 3% Gaussian noise to boxcar-filtered depth ionization curves. Repeat curve fitting to get SPR. Then evaluate $\frac{SPR(3\%noise)-SPR(1\%noise)}{(3\%-1\%)}$