An analysis of the physics-rich endgame of reionization at z = 5.7 is performed, utilizing jointly the observations of the Lyα forest, the mean free path of ionizing photons, the luminosity function of galaxies and new physical insight. We find that an upper limit on τ e provides a constraint on the minimum mean free path (of ionizing photons) that is primarily due to dwarf galaxies, which in turn yields a new and yet the strongest constraint on the matter power spectrum on 10 6 − 10 9 M scales. With the latest Planck measurements of τ e = 0.055 ± 0.009, we can place an upper limit of (8.9 × 10 6 , 3.8 × 10 7 , 4.2 × 10 8 ) M on the lower cutoff mass of the halo mass function, or equivalent a lower limit on warm dark matter particle mass m x ≥ (15.1, 9.8, 4.6)keV or on sterile neutrino mass m s ≥ (161, 90, 33)keV, at (1, 1.4, 2.2)σ confidence level, respectively.