Parameters of the inner engine of GRB 190114C. For this source we have L_GeV, 1 = 1.47 × 10⁵² erg s⁻¹ and E_GeV = 1.8 × 10⁵³ erg. Upper panel: family of solutions of B₀ as a function of α (blue curve), given by Eq. (27). We use here a photon energy ϵ_γ = 0.1 GeV (lower edge of the Fermi-LAT energy band). In the gray shaded region the mean free path is cm, while in the white shaded region it is cm. The curve separating the two regions is therefore given by the equality in (24). Lower panel: corresponding family of solutions M(α) (red curve), given by Eq. (21).