90% CL upper limits for the baryon equipartition parameter ϵ_p in the Northern (left) and Southern (right) Sky as a function of the magnetic equipartition ϵ_B. These constraints are obtained with the stacking analysis of the prompt catalog, assuming a neutrino spectral index γ = 2. Excluded values are shown as shaded regions for different values of the neutrino energy E_ν. Typical values of the timescale variability δt_obs = 0.1 s and redshift z = 1 are used to compute these limits. To derive ϵ_B, we assumed a typical observed spectrum of lGRB with the peak energy of 300 keV (see Eq. (31)). It is worth notice that the asymptotic value of ϵ_p in the low-magnetic field regime in the Southern Sky is consistent with the limits computed in Fig. 8 in the same hemisphere, assuming the same parameters.