Fig. 7

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Orbital evolution of selected long-term-stable solutions with similar astrometric fit quality, but exhibiting qualitatively different stability signatures. The left column is for the exact Laplace resonance, the middle column is for a model displaced from the PO but rigorously stable, and the right column is for a >1 Gyr stable solution characterized by rotation of one critical angle of the 2:1 MMR in the outermost pair. The rows from the top to bottom are for all critical angles of the 2:1 MMR, the critical angle of the generalized Laplace MMR, and eccentricities for subsequent pairs of planets. See Table 7 for the initial conditions labeled from 1 to 3 at the top-left corner of each column.
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