Mean of the absolute detectabilities (markers) as a function of the shape index (defined in Fig. D.1) at z = 0, for the simulations with massive neutrinos and variable σ₈, and its corresponding standard error (error bars). The results for the connected and reduced 3PCF ζ and Q are shown in the top and bottom rows, respectively. Each column corresponds to a different range of triangle scales, depending on the value of the largest triangle side s₂₃, as detailed in the label above each panel: small (5 h⁻¹ Mpc ≤ s₂₃ ≤ 30 h⁻¹ Mpc), intermediate (30 h⁻¹ Mpc ≤ s₂₃ ≤ 70 h⁻¹ Mpc), and large (70 h⁻¹ Mpc ≤ s₂₃ ≤ 145 h⁻¹ Mpc for ζ and 70 h⁻¹ Mpc ≤ s₂₃ ≤ 110 h⁻¹ Mpc for Q). The means are computed only for those shape indices that correspond to at least two populated (s₁₂/s₂₃, s₁₃/s₂₃) bins, depending on the considered scale range and the adopted binning of the side ratios. The schematic representation of triangles in the bottom-right panel qualitatively shows the mapping between the shape index and triangle shapes: low values correspond to equilateral and quasi-equilateral triangles, intermediate values (highlighted by the vertical gray band) to right-angled and quasi-right-angled triangles, and large values to elongated (squeezed/folded) triangles. The vertical axis shows only the mean detectability values below 3, to better highlight the differences between the lowest neutrino mass, M_ν = 0.1 eV, and the varying-σ₈ simulations.