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Fig. D.1

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Histograms of the semi-major axes, eccentricities, and inclinations of the HR 8799 systems, separated by planet. Panel (a): Isolated resonant systems. Orbital evolution oscillates around the initial conditions and the MMR chain is maintained. Panel (b): Perturbed resonant systems. The MMR chain is broken in some simulations. However, these broken MMR chains are often short-lived, so the initial MMR chain remains the only stable mode. Panel (c): Isolated non-resonant systems. Some of the systems diverge from the broken MMR chain and end up destroyed. The eccentricities are not as sharply bound as the resonant systems. Shifts in inclination occur despite the systems being planar and isolated. This should not happen as there is no possible force to drive the planets off the plane. We believe this results from the chaotic growth of numerical errors, as these systems not only live in 2D space, but also are randomly orientated in 3D space. Panel (d): Perturbed non-resonant systems. States that diverged from the broken MMR chain are more prominent than in panels b and c. HR 8799 d and HR 8799 b show an apparent second stable mode, but this only occurs in a single simulation. The broken MMR chain remains the most prominent feature. The dataset of each of the histograms contains all states of all its relevant simulations. These amount to 10000 states per simulation, with one simulation for panel (a), and 50 simulations for panels (b), (c), and (d). By including all states instead of just the final state, longer-lived states become more prominent even if these states are not the final state.

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