Data and results of simulation A at time t_A, 1 = 400 Myr. The four panels show: (a) the true and inferred gravitational potentials; (b) the two-dimensional data histogram d_i, j in the (Z, W)-plane; (c) the phase-space spiral as extracted from the data (see Eq. (25) for the precise definition) and smoothed to an effective bin size of (40 pc)×(2 km s⁻¹); and (d) the best fit spiral density S(Z + Z_⊙, W + W_⊙ | Ψ_spiral), as defined in Eq. (26). Panel a: the height is plotted in the range Z ∈ [ − 700, 700] pc, corresponding to the outer limit of the mask function; in all other panels, the range is Z ∈ [ − 900, 900] pc. Panels c and d: the outer boundary corresponds to that of the mask function of Eq. (17); panel d: the inner boundary corresponds to the lower limit in vertical energy for the spiral model, according to Eq. (14).