The X-ray binary pulsar XTE J1829-098 has been observed at extremely low luminosities for its spin period of 7.8448 s. Although its distance is uncertain by a factor of 4, the lowest observed X-ray fluxes may not correspond to its minimal-accretion propeller state or to nonaccreting states occurring at even lower X-ray luminosities, in which case the source has been caught at the bottom of the Corbet gap. We analyze all proposed distances D to the binary and the lowest X-ray fluxes, and we find only two physically acceptable solutions: (a) For D = 4.5 kpc (if the companion is a main-sequence B0 star), the neutron star is canonical with mass 1.41 M ⊙, radius 10.1 km, and a purely dipolar magnetic field as indicated by a cyclotron absorption line detected at 15 keV. In this case, the source has been observed at the bottom of the Corbet gap, the third high-mass X-ray binary pulsar to be caught in this state after the “twins” 4U 0115+63 and V 0332+53 found by Tsygankov et al. (b) For D = 18 kpc (if the companion is a B0.5Ib supergiant), the neutron star is ultramassive with mass 2.62 M ⊙, radius 18.7 km, and a dominant nondipolar magnetic field B mul = 1.26 TG (versus a dipolar component of only B dip = 0.43 TG). In this case, the source has been observed in its propeller state.