Free-form potential reconstructions using Planck TT+TE+EE+lowE+lensing (Sect. 5.4). Top-right panel: Bayes factors for the free-form potential reconstruction. The preferred reconstruction has N = 1, corresponding to a constant non-zero d²lnV₁/dϕ². The remaining panels show reconstructions for the N = 8 knot case, focusing on the scalar primordial power spectrum, and the inflationary slow-roll parameters ε_V and η_V. Red lines indicate sample trajectories from the prior, whilst black lines are from the posterior. Technically the slow-roll parameters are defined as functions of ϕ, but we instead substitute this for the Hubble-radius-exit value to make for clearer comparison between posterior samples. In all plots, the approximate link between ℓ and k is via the Limber approximation, ℓ ≃ k/D_A, where D_A = r_*/θ_* is the comoving angular distance to recombination, which is at comoving distance r_*.