derived from experiments on synthetic chondritic compositions (Andrault et al. 2011), while at lower pressures the melting relations follow the peridotite-based parametrization compiled by Hamano et al. (2013).

These datasets are smoothly joined to provide continuous melting curves across the mantle.
2.6.

Effect of fO2 on mantle solidus Building on the thermodynamic framework provided by the adopted equations of state, we now describe how variations in oxygen fugacity influence mantle melting relations.

The melting temperature of the mantle depends sensitively on its composition and thermodynamic state, which are strongly regulated by redox conditions.

Laboratory measurements by Lin et al. (2024)
3.2 ∆log fO2, (10) With ∆logfO2 being the difference in log units between IW+2.0 (reference solidus) and the target fO2,and the ±383 K term reflects the experimental uncertainty on the solidus temperature derived from the Lin et al. (2024) measurements.

This would imply that very reducing mantles like the early Earth (fO2 ≈IW–4.0) should have a significantly higher melting temperature, whereas more oxidizing conditions lead to a lower melting temperature.

This suggests that melting processes, redox evolution, outgassing, atmospheric composition and greenhouse effects form an emergent, coupled system that cannot be treated piecewise in isolation.

To investigate these coupled interactions, we applied the Lin et al. (2024) redox-dependent shift (Equation 10) to the baseline melting curves used in our thermophysical model (Section 2.5).

In this study, the applied offsets produce the expected monotonic trend: reducing conditions (IW–4.0) shift the melting curves to higher temperature, whereas oxidizing conditions (IW+4.0) shift them to lower temperature.

Because robust parametrizations describing the redox dependence of the liquidus are currently unavailable due to the limited experimental constraints, we applied the same temperature offset derived for the solidus to the liquidus for each redox state.

This preserves the relative separation between solidus and liquidus while shifting the melting interval consistently with redox conditions.

The resulting set of redox-dependent melting curves is shown in Fig. 2.

In our framework, these redox-dependent melting curves provide a convenient parametrization of melting behaviour as a function of redox state and are used directly within SPIDER to compute the melt fraction.

We noted, however, that oxygen fugacity is fundamentally an outcome of thermodynamic equilibrium rather than an independently imposed parameter.

During magma ocean evolution, melting induces phase separation and element partitioning, which can modify the Fe3+/Fe2+ ratio and hence the effective fO2, leading to a corresponding evolution of the melting relations themselves.

In this work, we therefore adopted a simplified approach in which redox-dependent offsets to the melting curves are prescribed, and should be interpreted as a first-order approximation to this coupled thermochemical behaviour.

Because the oxidation state of the mantle is likely inhomogeneous with pressure, we incorporated two distinct effects of fO2 that reflect two different physical roles of redox state during magma–atmosphere evolution.

In both cases, we explored the same range of redox conditions (IW–4.0, IW–2.0, IW+0, IW+2.0, IW+4.0), allowing us to connect interior melting behaviour with surface outgassing.

The individual effects of these two fO2 terms are detailed as follows:
1.

Deep-mantle oxidation state fOmelt
controlling the melting curves. fOmelt
enters our model through the redox-dependent shift of the melting curves, as described in Section 2.6; we applied the chosen value of fO2 to adjust the melting curve used by the interior model.

This fOmelt
value expresses the thermophysical and compositional state of the interior.

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[Table: Table 1. Overview of the parameter space explored in this study.]

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