The distribution of the population on the characteristic log₁₀(L₀/L_ch)–log₁₀(τ₀/t_ch) plane. The left panel shows a single random realization of the synthetic PWN population containing 1600 sources on the plane, with ellipses marking the isolevels enclosing 10, 50, and 98 percent of the population. Each point is color-coded by density, derived from Gaussian KDE, with colors ranging from red (denser regions) to blue (sparser ones). The right panel displays the same plane along with the isolevels, but color-coded by the CF (CF = R_max/R_min) at the first compression, as indicated in the color bar. In this plot, only PWNe in the post-compression phase are shown. Colored triangles in this plot highlight two example PWNe within a 50% enclosing ellipse with different CFs used for individual simulations. Straight lines in both plots denote loci of four constant pulsar–SNR energetics.