  Studies of close-in planets orbiting M dwarfs have suggested that the M dwarf
radius valley may be well-explained by distinct formation timescales between
enveloped terrestrials, and rocky planets that form at late times in a
gas-depleted environment. This scenario is at odds with the picture that
close-in rocky planets form with a primordial gaseous envelope that is
subsequently stripped away by some thermally-driven mass loss process. These
two physical scenarios make unique predictions of the rocky/enveloped
transition's dependence on orbital separation such that studying the
compositions of planets within the M dwarf radius valley may be able to
establish the dominant physics. Here, we present the discovery of one such
keystone planet: the ultra-short period planet TOI-1634 b ($P=0.989$ days,
$F=121 F_{\oplus}$, $r_p = 1.790^{+0.080}_{-0.081} R_{\oplus}$) orbiting a
nearby M2 dwarf ($K_s=8.7$, $R_s=0.45 R_{\odot}$, $M_s=0.50 M_{\odot}$) and
whose size and orbital period sit within the M dwarf radius valley. We confirm
the TESS-discovered planet candidate using extensive ground-based follow-up
campaigns, including a set of 32 precise radial velocity measurements from
HARPS-N. We measure a planetary mass of $4.91^{+0.68}_{-0.70} M_{\oplus}$,
which makes TOI-1634 b inconsistent with an Earth-like composition at
$5.9\sigma$ and thus requires either an extended gaseous envelope, a large
volatile-rich layer, or a rocky portion that is not dominated by iron and
silicates to explain its mass and radius. The discovery that the bulk
composition of TOI-1634 b is inconsistent with that of the Earth favors the
gas-depleted formation mechanism to explain the emergence of the radius valley
around M dwarfs with $M_s\lesssim 0.5 M_{\odot}$.
