Empirical BDF and dynamical operator for the orbital period, P. The panel layout is analogous to Fig. 3. A clear cut-off is seen around 10⁷ days; model fitting is restricted to P > 2 days, where dynamical effects dominate over stellar evolution. A slight deviation is visible around E_b ≈ 10⁵–10⁶, reflecting a limitation of our model in accurately capturing the evolution of binaries in this period range.