Distribution of 1,000 randomly sampled NS posteriors from the coplanar inclined model (see Fig. A.2) integrated over 10,000 years. The two-dimensional contours represent the 1-, 2-, and 3-σ confidence intervals of the stable posterior distribution. From top to bottom, the corner plot shows the mean osculating planetary eccentricities and osculating eccentricity semi-amplitudes for the three planets, pivotal for assessing the GJ 581 system’s dynamical properties. The median values of the complete posterior distributions are indicated by red lines.