**3. Results**

We here clarify that the purpose of our analysis is to show how similar our results are, compared to other ones in the literature given that our sample size differs from other studies for *E*iso and *T* ∗ <sup>90</sup> (our sample has 80 GRBs), while this is the first time in the literature that we compare the results for the *L*a,radio and *T* ∗ a,radio (our sample has 18 GRBs) with the previous results in the literature performed in X-rays and optical. This is an essential comparison to allow the determination of the intrinsic nature of the *L*a,radio and *T* ∗ a,radio correlation and to check for the universality of the results related to the evolutionary functions for these variables with the EP method.

Using the procedure outlined above, we correct log *E*iso, log *T* ∗ <sup>90</sup> using the formulation log *E* 0 iso = log *E*iso − log((1 + *z*) *<sup>δ</sup>E*iso ) and log *T* ∗ 0 <sup>90</sup> = log *T* ∗ <sup>90</sup> − log((1 + *z*) *δT* ∗ <sup>90</sup> ), where all quantities that have 0 symbol are the variables for which the evolution has been removed, thus they are no longer dependent on the redshift. We find *δ<sup>T</sup>* ∗ 90 = −0.65 ± 0.27, with the 1 *σ* errors defined as the average of the values of *τ* = 1 and *τ* = −1, and *δE*iso = 0.39 ± 0.88. Figure 3 shows these results—the top left panel shows log *T* ∗ <sup>90</sup> for the sample of 80 GRBs as a function of redshift, with the limiting value shown in red. The top right panel highlights the evolutionary function for log *T* ∗ <sup>90</sup>, with dashed lines at *τ* = 0, ±1. The same plots for log *E*iso are shown in the bottom panels.

**Figure 3.** The (**upper left**) panel shows the values of log *T* ∗ <sup>90</sup> vs. redshift in blue and the limiting log *T* ∗ <sup>90</sup> in the rest-frame in red. The (**upper right**) panel shows the Kendall *τ* vs. the slope of the evolutionary function with 1 *σ* errors shown with dashed blue lines. As with the upper panels, the (**lower left**) panel shows values of log *E*iso vs. redshift in blue with the limiting line in red, and the (**right**) panel shows the Kendall *τ* vs. slope of the evolutionary function with 1 *σ* errors as dashed blue lines.

For the plateau sample of 18 GRBs, we use the same formulation to obtain log *L* 0 a,radio = log *L*a,radio − log((1 + *z*) *<sup>δ</sup>L*a,radio ) and log *T* ∗ 0 a,radio = log *T* ∗ a,radio − log((1 + *z*) *δT* ∗ a,radio ). We find the values of *δ* for log *L*a,radio and log *T* ∗ a,radio as *δ<sup>T</sup>* ∗ a,radio = −1.94 ± 0.86 and *δL*a,radio = 3.15 ± 1.65. These results are shown in Figure 4—log *T* ∗ a,radio as a function of redshift is shown in the top left panel, with the limiting values in red. The evolutionary function is shown in the top right panel, with dashed blue lines at *τ* = 0, ±1. The bottom two panels display the same plots for log *L*a,radio.

**Figure 4.** The (**upper left**) panel shows the values of log *T* ∗ a,radio vs. redshift in blue and the limiting log *T* ∗ a,radio in the rest-frame in red. The (**upper right**) panel shows the Kendall *τ* vs. the slope of the evolutionary function with 1 *σ* errors shown with dashed blue lines. As with the upper panels, the (**lower left**) panel shows values of log *L*a,radio vs. redshift in blue with the limiting line in red, and the (**right**) panel shows the Kendall *τ* vs. slope of the evolutionary function with 1 *σ* errors as dashed blue lines.
