Nonparametric reconstruction of the dark energy equation of state w(z) for different assumed matter densities in the joint DESI+DESY5 analysis. Top: reconstructed w(z) assuming Ω_m,0 = 0.26,  0.30,  0.34, with the red dashed line indicating the ΛCDM value w = −1. Middle and bottom: the numerator and denominator of the reconstruction formula, respectively, showing that while the numerator varies smoothly, the denominator can approach zero and induce the nonphysical divergences observed in the top panel.