Confrontation between tidal survival limits and the close-in planet population. (a) Period–radius plane. The solid black curve traces the Neptunian desert boundary, and the vertical dashed line marks the ridge limit (Castro-González et al. 2024a). Dashed red and blue curves show tidal survival boundaries P_tide(R_p; q) for the q = 0.84 and q = 0.16 mass–radius envelopes, adopting η = 4.5, and the shaded region indicates the survival band. Dotted curves show representative $P_{\mathrm{circ}}^{max}$ tracks with $Q{\prime }_{\mathrm{p}}={10}^5$ and M_★ = 1 M_⊙ (Owen & Lai 2018): orange and red correspond to t_sys = 8 and 4 Gyr with a₀ = 1.5 au along the q = 0.84 envelope, and blue to t_sys = 8 Gyr with a₀ = 1.0 au along the q = 0.16 envelope. Dash-dotted dark magenta and pink curves show illustrative secular-chaos circularisation curves (e.g. Matsakos & Königl 2016), computed using M(R_p; q = 0.5) and perturbing-companion masses of 0.7 and 0.4 M_J, respectively. (b) Mass–radius plane with the quantile envelopes M(R_p; q).