tentatively ruling out case 3 for each planet, unless the atmospheric vertical mixing is low (Figure 4).

TOI-776 c additionally has a lower limit on mean molecular weight of > 6 – 8 g mol−1 if high altitude aerosols are not responsible for the featureless spectrum (Teske et al. 2025), which could suggest case 3 with a low vertical mixing strength when combined with the upper limit from He escape.

GJ3090 b has also been a subject of interest for breaking the cloud-mean Article number, page 7 molecular weight degeneracy (Ahrer et al.

2025), leading to a lower limit of > 7.1 g mol−1, however if aerosols can be formed around µbar pressures then the mean molecular weight remains unconstrained (Parker et al. 2025).

In general, distinguishing cases 1 and 2 (formation within the water ice line) from cases 3 and 4 (formation beyond the water ice line) can be done based on mean molecular weight, with the added consideration of H2O condensation in the colder population, exemplified by K2-18 b.

Distinguishing case 1 from case 2 is more ambiguous and will require better observational and modeling constraints on the wider carbon chemistry involving CO and CO2, which is dependent not only on the different formation cases but also on the atmospheric temperature profile, vertical mixing strength, and photochemistry (Figure 4).

Distinguishing case 3 from case 4 might appear straightforward due to the different mean molecular weight atmospheres that they predict, however equilibrium chemistry at different TAMOI, and disequilibrium chemistry over the vertical extent of the atmosphere can each significantly alter the mean molecular weight of case 3 atmospheres, blurring the observational identifiers of soot-water-rock formation with only waterrock formation scenarios (Figure 5).

Unambiguously, however, CH4-rich atmospheres can only be achieved by formation beyond the water ice line, while H2O-rich atmospheres without significant CH4 are counterintuitively indicators of formation within the water ice line.

In summary, Figure 5 reveals a clear compositional trend from volatile-poor to volatile-rich formation scenarios.

The equilibrium solution space traces an approximately linear sequence in log-log space, where H2O/CH4 and MMW serve as the primary diagnostic: low H2O/CH4 and high MMW identify volatile-rich accretion beyond the water ice line (cases 3 and 4), while high H2O/CH4 and low MMW indicate volatile-poor accretion within the water ice line (cases 1 and 2).

Two processes can cause planets to deviate from this in-equilibrium trend.

First, in sufficiently cool atmospheres, H2O condensation removes water from the observable upper atmosphere, shifting apparent H2O/CH4 ratios to lower values, as observed for K2-18 b.

Second, fractionated atmospheric escape preferentially removes hydrogen, elevating the mean molecular weight and displacing planets toward higher MMW at fixed H2O/CH4, as possibly exemplified by GJ9827 d near the radius valley.

Accounting for these two effects, the H2O/CH4 ratio and mean molecular weight together provide a powerful twodimensional diagnostic for sub-Neptune formation history that is broadly consistent with the current JWST population.
3.2.1.

Carbon dioxide as additional discriminant in K2-18 b and TOI-270 d The two well-characterized sub-Neptunes K2-18 b and TOI-270 d provide constraints on carbon- and oxygen-bearing species beyond H2O and CH4, and in particular on CO2, which our models suggest may help discriminate between formation scenarios.

For K2-18 b, multiple independent retrieval studies consistently report significant CO2 detections, with inferred log-abundances spanning roughly −6 to −2 and C/O ratios ranging from moderately to strongly super-solar (Fernández-Rodríguez et al. 2026; Schmidt et al. 2025).

For TOI-270 d, the retrieved carbon-species abundances are Article number, page 8
more tightly clustered, with both log(CO2) and log(CH4) typically falling between −3 and −1.

C/O ratios are generally approximately solar to super-solar, with individual retrieval cases reaching values as high as 3.21+6.1 −1.9 (Felix et al. 2025b), and atmospheric metal mass fractions are consistently high, with representative values around Zatm ∼0.6.

The CO2 abundances further confirm the conclusion drawn from H2O/CH4 in Section 3.2: both planets strongly disfavour water-poor formation pathways (cases 1 and 2).