Left panels: Density and Brunt-Väisälä frequency profiles of two smoothed 1 M_⊙ models, A (Gaussian parameters: amplitude = 9e−10 s⁻², width = 7e6 cm) and B (Gaussian parameters: amplitude = 6e−10 s⁻², width = 2e7 cm) around the He-flash discontinuity, compared to the model with a sharp transition. Right panels: Period-spacing structure of mode frequencies for the smoothed models A and B (red dots), compared to the sharp transition model (grey dots).