Top: reconstructed shape of the single-field inflaton potential from the cubic-spline power spectra mode-expansion using 12 knots and the Planck TT,TE,EE+lowE+lensing+BK15+BAO data. Bottom: result when r is fixed at 0.001. Instead of plotting as a function of wavenumber k we plot lnV(ϕ)/V_pivot about a pivot field value ϕ_pivot. Note that the range on the ϕ axis is quite different for the small r case than the floating case. The probability of local convexity evaluated at ϕ_pivot is denoted as p(convex).