Flow chart indicating the inversion process of the radiative transfer equation (RTE) for polarized light (i.e., the Stokes inversion) combined with MHS constraints. The black squares denote the acquisition of the observed Stokes vector 𝕀^obs(x, y, λ) and the determination of an initial set of physical parameters (T⁰⁰(x, y, z), B⁰⁰(x, y, z)) with which we can start the inversion (i.e., a guess). The red squares indicate the inversion process as carried out by the Firtez-DZ code. This is described in detail in Sect. 3.1. Blue squares correspond to the steps carried out by the MHS module (see Sect. 3.3 for details). Finally, green squares and arrows indicate locations where an interplay between Firtez-DZ and the MHS module are needed in order to assess if convergence and exit conditions are achieved (see Sect. 3.4 for more information).