Constraints on the

Context. JWST provides a unique dataset for studying the earliest stages of reionisation at z > 9, promising insights into the first galaxies. Many JWST/NIRSpec prism spectra of z > 5 galaxies have revealed smooth Lyman-alpha breaks, implying damping wing scattering by neutral hydrogen. Aims. We investigate what current prism spectra imply about the intergalactic medium (IGM) at z > 6 and how best to use NIRSpec spectra to recover IGM properties. We use a sample of 99 z ∼ 5.5 − 13 galaxies with high S/N prism spectra in the public archive, including 12 at z > 10. Methods. We analyse these spectra using damping wing sightlines from inhomogeneous reionising IGM simulations, mapping between the distance of a source from the neutral IGM and the average IGM neutral fraction. We marginalise over absorption by local neutral hydrogen around the galaxies and Lyman-alpha emission. Results. We observe a decline in the median and variance of flux around the Lyα break with increasing redshift, consistent with an increasingly neutral IGM, as ionized regions become smaller and rarer. At z ≳ 9 the spectra become consistent with an almost fully neutral IGM. We find S/N > 15 per pixel is required to robustly estimate IGM properties from prism spectra. We fit a sub-sample of high S/N spectra and infer mean IGM neutral fractions of $ \overline{x}_{{\small { {\text{HI}}}}} = 0.33^{+0.18}_{-0.27}, 0.64^{+0.17}_{-0.23} $ (> 0.70 excluding GNz11) at z ≈ 6.5, 9.3. We also investigate local HI absorption, finding a median column density of log10NH I ≈ 1020.8 cm−2, comparable to z ∼ 3 Lyman-break galaxies, with no significant redshift evolution z ≳ 5.5. We find galaxies showing the highest column density absorption are more likely to be in close associations of sources (≲500 pkpc), implying absorption is enhanced in massive dark matter halos. Future deep prism and grating spectroscopy of z > 9 sources will provide tighter constraints on the earliest stages of reionisation, key for understanding the onset of star formation.