Mass proxy in cosmological analysis. Left panel: Mass-observable distribution of galaxy clusters in our mock catalogue. The grey shaded region represents the mass selection of our sample, excluding clusters with M_vir < 10¹⁴ M_⊙ h⁻¹. Right panel: Marginalised posterior distributions in the Ω_m − σ₈ plane, with 68% and 95% confidence intervals, using a binwidth of Δz = 0.4, in redshift space. The red contour shows the result for the two-point correlation function monopole, while the blue contour accounts also for the effect of the mass-observable scaling relation. The dashed lines indicate the Ω_m and σ₈ values of the PINOCCHIO simulation, while the dot-dashed line shows the predicted S₈ degeneracy curve.