Rotated action space for metallicities between -4.0 ≤ [Fe/H] < -1.7. The grey dashed lines correspond to different values of L_z/J_tot: [-0.95, -0.8, -0.5, 0, 0.5, 0.8, 0.95]. Left column: decontamination process and folding using LAMOST contamination. Top row: density of spectroscopic contaminants. Middle row: pixel-by-pixel decontamination. Bottom row: folding of the retrograde components over the prograde components, for PGS decontaminated pixel-by-pixel. In this space, the folding axis of symmetry is the grey dashed line at L_z/J_tot = 0. Right column: same as the left panels, but the three actions were computed shifting the observed V_ϕ by 40 km.s⁻¹. Same as Fig. 15 of Sec. 6.2.