The first (nearly) model-independent constraint on the neutral hydrogen fraction at

Cosmic reionization is expected to be complex, extended and very inhomogeneous. Existing constraints at z ∼ 6 on the volume-averaged neutral hydrogen fraction, ⁠, are highly model-dependent and controversial. Constraints at z < 6, suggesting that the Universe is highly ionized, are also model-dependent, but more fundamentally are invalid in the context of inhomogeneous reionization. As such, it has recently been pointed out that there is no conclusive evidence that reionization has completed by z ∼ 5–6, a fact that has important ramifications on the interpretation of high-redshift observations and theoretical models. We present the first direct upper limits on at z ∼ 5–6 using the simple and robust statistic of the covering fraction of dark pixels in the Lyα/β forests of high-redshift quasars. With a sample of 13 Keck Echellette Spectrograph and Imager spectra we constrain at 5.0 ≲ z ≲ 5.5, rising to at z ∼ 6.1. We also find tentative evidence for a break in the redshift evolution of the dark covering fraction at z ∼ 5.5. A subsample of two deep spectra provides a more stringent constraint of ⁠, when combined with conservative estimates of cosmic variance. This upper limit is comparable to existing results at z ∼ 6 but is more robust. The results presented here do not rely on assumptions about quasar continua, intergalactic medium density, the morphology of H ii regions or ionizing background fields, and thus are a good starting point for future interpretation of high-redshift observations.