The λ and ﹩v\sin {i}_{\star }﹩ distributions, along with derived T_eff boundaries. Panel (a): λ distribution for hot-Jupiter systems with confirmed or candidate stellar companions. The T_eff boundary of ﹩610{5}_{-133}^{+123}﹩ K is marked with a black dashed line, with shaded 1σ interval. Panel (b): same as the top panel, but for single-star hot-Jupiter systems with T_eff boundary = ﹩644{7}_{-119}^{+85}﹩ K. Panel (c): ﹩v\sin {i}_{\star }﹩ distribution for single stars, compiled following the updated prescription described in A. C. Beyer & R. J. White (2024). The resulting T_eff boundary is ﹩65{10}_{-127}^{+97}﹩ K, consistent with that derived from the single-star λ distribution. Panel (d): same as panel (c), but for binary and multiple-star systems.