Does Cumulative XUV Unify the Neptunian Desert?

The Neptunian desert is the scarcity of roughly 2 - 10,R planets on orbits of a few days. Atmospheric escape driven by stellar X-rays and extreme-ultraviolet (XUV) radiation may shape its lower boundary by stripping hydrogen-helium envelopes. Because M dwarfs and F-, G-, and K-type stars have different activity histories, present bolometric irradiation may not trace the cumulative high-energy dose that drives escape. We ask whether cumulative XUV yields a common boundary across spectral type and whether the convergence survives star-to-star variation in age and rotation. Using 1850 Kepler and TESS planets, Model for Rotation of Stars (MORS) activity tracks, and a global boundary model, we find that the offset between M dwarfs and FGK stars shrinks from-1.065 dex in bolometric flux to-0.369 dex for a common 5 Gyr median-rotation XUV history. Assigning plausible ages and initial rotations to individual hosts preserves the smaller XUV offset in every trial, with a median reduction of 69.1%. A common-period null yields comparable alignment. Cumulative XUV therefore substantially reduces the host-type dependence, but the present data do not establish a universal XUV threshold independent of orbital period.