– 6 – 0.1 0.15 0.2 0.25 0.3 10 20 30 0 1 2 3 4 0 1 2 3 4 0.1 0.15 0.2 0.25 0.3 0 1 2 3 4 Fig. 1.— Models for the evolution of KOI-74 and KOI-81 that invoke stable mass transfer. Top panels: Orbital period versus the mass of the white dwarf. Black dots show the full range of predictions in this paper. Triangles with uncertainty limits show the mass measurements of R2010 (cyan) and vK2010 (red). Green points and uncertainty limits show the mass-transfer model predictions of vK2010. Note that, in addition to the lower limits shown, derived for a tidal-perturbation model, R2010 provide lower limits in the brown dwarf range; these would not be consistent with the formation of the systems through stable mass transfer. Bottom panels: Initial mass M 2 (0) of the secondary versus the initial mass M 1 (0) of the primary for the steady mass transfer model used in this paper ( § 2). These are the initial states consistent with the present-day binarity parameters of KOI-74 and KOI-81. If