The waiting-time dependent residuals differ in shape between the 2020 and 2021 data around the 0-1 peak (Videos S8 and S9), but for frequencies less than 2035 cm -1 are similar around the diagonal, particularly at early waiting times. Differences around the 0-1 peak likely cause the discrepancies in the CLS decays shown in Figure . To show this more clearly, we overlay the centerlines of the experimental spectra in the left and right panels of Videos S8 and S9. Close inspection of the right panel in Video S8 reveals the structured feature responsible for the slower CLS decay in the 2020 data which is not present in the 2021 data (Video S9). We must caution against over interpreting the residual here. One should not conclude that the residual reflects the "unmodeled" part of the lineshape where the model 𝐌𝐌(𝐩𝐩) and Jacobian 𝐉𝐉 are nonzero. The best fit model is influenced by both "modeled" and "unmodeled" parts of the experimental lineshape such that C(𝐩𝐩) is minimized. On the other hand, in the region below 2135cm -1 along the diagonal, the residual does accurately reflect the "unmodeled" lineshape because 𝐌𝐌(𝐩𝐩) and 𝐉𝐉 are virtually zero and therefore the residual 𝐫𝐫 in this region cannot influence the model fit by Eq. 4.