It has recently been shown that stellar clustering plays an important role in shaping the properties of planetary systems. We investigate how the multiplicity distributions and orbital periods of planetary systems depend on the 6D phase space density of stars surrounding planet host systems. We find that stars in high stellar phase space density environments (overdensities) have a factor 1.6 - 2.0 excess in the number of single planet systems compared to stars in low stellar phase space density environments (the field). The multiplicity distribution of planets around field stars is much flatter (i.e. there is a greater fraction of multi-planet systems) than in overdensities. This result is primarily driven by the combined facts that: (i) `hot Jupiters (HJs) are almost exclusively found in overdensities; (ii) HJs are predominantly observed to be single-planet systems. Nevertheless, we find that the difference in multiplicity is even more pronounced when only considering planets in the Kepler sample, which contains few HJs. This suggests that the Kepler dichotomy -- an apparent excess of systems with a single transiting planet -- plausibly arises from environmental perturbations. In overdensities, the orbital periods of single-planet systems are smaller than orbital periods of multiple-planet systems. As this difference is more pronounced in overdensities, the mechanism responsible for this effect may be enhanced by stellar clustering. Taken together, the pronounced dependence of planetary multiplicity and orbital period distributions on stellar clustering provides a potentially powerful tool to diagnose the impact of environment on the formation and evolution of planetary systems.
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