A Stacking Analysis of Faint Short GRBs Observed by Fermi-LAT and Cooling-Regime Constraints on GRB 090510

We perform a stacking analysis of 15 faint short GRBs observed by Fermi-LAT and compare their $>100$~MeV afterglow with GRB~090510. Because individual faint bursts contain only a few selected LAT photons, stacking is required to measure their average temporal behavior. The stacked light curve decays as α = 0.89 ± 0.06, consistent with, though not uniquely diagnostic of, a slow-cooling forward-shock interpretation. In contrast, GRB~090510 shows two much steeper decay phases, α₁ = 2.13 ± 0.24 and α₂ = 2.31 ± 0.81, after accounting for a possible plateau-like feature, indicating that it is not representative of the faint short-GRB population. If the LAT band lies above the cooling frequency, the condition hνc < 0.1~GeV gives εB 3×10⁻⁴-7×10⁻³ for n~10⁻⁵-10⁻³~cm⁻³. GRB~090510 may therefore be an unusual event, possibly involving efficient magnetic-field amplification, favorable viewing geometry, or additional emission components.