Left: Upper limit on the [O III] 88 μm luminosity of GLASS-z13 as a function of its SFR, compared to galaxies at z = 6 − 10 taken from the literature compilation by Harikane et al. (2020). Upper limits are presented for the two respective SFRs derived by Castellano et al. (2022) and Santini et al. (2022). If GLASS-z13 is a z > 11.9 galaxy, the upper limits are consistent with the empirical trend. Right: CLOUDY calculation results taken from Harikane et al. (2020) for the ratio between [O III] 88 μm luminosity and SFR, as a function of ionisation parameter U_ion, as well as the ISM metallicity and density. Under the assumption that GLASS-z13 is a z ≈ 12 − 13 galaxy, the upper limits on the [O III] 88 μm luminosity–SFR ratio that would be obtained for the two SFRs derived in the literature are indicated by the dashed black and grey lines with arrows. A broader line width of ∼400 km s⁻¹ would move the upper limits up by a factor of two. These upper limits suggest either a low-metallicity (< 0.2 Z_⊙) and/or a dense (at least 100 cm⁻³) ISM.