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tokens: of Trappist-1f from a magma ocean phase to present assuming the modern surface volatile inventory exceeds 1 GPa (ocean depth >∼100 km). Figure 4. Trappist-1f’s coupled redox–thermal–climate evolution. The model is applied from magma ocean to present with initial water inventories ranging from 30–300 Earth oceans (∼1–10 GPa), and initial CO 2 inventories ranging from 20 to 6000 bar. The lines are median values and shaded regions denote 95% confidence intervals across all model runs. The coupled model includes (a) mantle and surface temperature evolution, (b) the solidification of the magma ocean from core to surface, (c) atmospheric evolution, (d) surface ocean condensation, (e) surface energy budget, (f) CO 2 outgassing and weathering fluxes, (g) crustal production, (h) mantle redox state, and (i) the surface redox budget. Despite the large pressure overburden from the surface ocean, crustal production may persist for billions of years due to mantle hydration suppressing the silicate solidus (g). Nonetheless, Trappist-1f does not experience magmatic outgassing due to the high solubility of volatiles in melt at GPa pressures (f), (i). According to this model, Trappist-1f ought to have experienced a ∼100 Myr magma ocean due to the extended pre-main sequence of Trappist-1 (Figure 4 (b)); absorbed shortwave radiation exceeds the runaway greenhouse limit for the first ∼100 Myr of Trappist-1f’s evolution (Figure 4 (e)). During this long-duration magma ocean phase, loss of hydrogen to space oxidized the mantle (Figure 4 (h)), consistent with previous models of magma ocean evolution on planets around M dwarfs (Schaefer et al. 2016 ; Wordsworth et al. 2018 ; Barth et al. 2020 ). Once absorbed shortwave radiation drops below the runaway greenhouse limit, the magma ocean freezes and a deep liquid water ocean condenses out of the steam atmosphere (Figure 4 (d)). Despite the large pressure overburden from this surface ocean, melt production may persist to the present (Figure 4 (g)). This is because crustal hydration reactions and subduction deliver water to the interior (Figure 4 (i)), suppressing the silicate solidus and hence allowing for partial melting. However, despite high crustal production rates, there is no magmatic outgassing throughout Trappist-1f’s evolution (Figures 4 (f), (i)) due to the high solubility of volatiles at GPa pressures. 4. Discussion To what extent is the simple melt-gas equilibrium partitioning approach described here a reasonable representation of waterworld degassing? Outgassing fluxes from magmatic sources are determined by the integrated loss of volatiles over the decompression path from the mantle to the surface as magma ascends and cools (Edmonds Woods 2018 ). The decompression path reflects changes in volatile solubilities as magma ascends from its mantle source to the surface. Solubilities typically decrease with decreasing pressure, which leads to degassing of volatiles along the decompression path (so-called “first