Forward models used to define the priors for the climate-constrained inversion. Left: bare-rock emission spectra for several plausible surface compositions, compared to blackbody surfaces with A_s = 0 and A_s = 0.4. These models motivate our uniform prior on surface albedo between 0 and 0.4. Right: emission spectra for 1 bar atmospheres composed of O₂, N₂, or CO, all with surface albedos of 0.2. These simulations have nearly identical emission spectra, motivating our treatment of O₂ as a proxy for other optically thin gases such as N₂ and CO.