Rest-frame NUV–r versus r–J color–color diagram for all BGGs combined across the full redshift range z = 0 to z = 4. Points are color-coded by their log₁₀(sSFR/yr⁻¹). Magenta lines delineate the quiescent region defined by $M_{\mathrm{NUV}}-M_r>3(M_r-M_J)+1$ and $M_{\mathrm{NUV}}-M_r>3.1$. Open red and blue squares denote BGGs classified as quiescent and star-forming, respectively, under both color and sSFR criteria. Star-forming BGGs dominate at higher redshifts (z ≳ 2), while the fraction of quiescent systems increases at lower redshifts. Full redshift-binned versions of this diagram (in Δz = 0.5 steps) are available in Section 6.