C/O ratio vs. orbital period and model comparison. Left: Monte Carlo–averaged fits comparing two models for the planetary C/O ratio as a function of the orbital period: a constant model (M₀; blue) and a log-linear model (M₁; orange). Each curve shows the median fit with shaded ±1σ bands across 10⁵ trials, and the black points mark the median and ±34.1% range within logarithmic period bins. Right: distribution of ΔAIC = AIC(M₀) − AIC(M₁) from 10⁵ Monte Carlo realizations, with the median (blue) and the null reference line at ΔAIC = 0 (orange dashed). Positive ΔAIC values indicate that the log-linear model provides a statistically better description of the data than the constant model.