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The angular momentum deficit (AMD) of a planetary system is a measure of itsorbital excitation and a predictor of long-term stability. We adopt theAMD-stability criteria to constrain the orbital architectures for exoplanetarysystems. Previously, He, Ford, & Ragozzine (2019) (arXiv:1907.07773v2) showedthrough forward modelling (SysSim) that the observed multiplicity distributioncan be well reproduced by two populations consisting of a low and a high mutualinclination component. Here, we show that a broad distribution of mutualinclinations arising from systems at the AMD-stability limit can also match theobserved Kepler population. We show that distributing a planetary system'smaximum AMD amongst its planets results in a multiplicity-dependentdistribution of eccentricities and mutual inclinations. Systems withintrinsically more planets have lower median eccentricities and mutualinclinations, and this trend is well described by power-law functions of theintrinsic planet multiplicity ($n$): $\tilde{\mu}_{e,n} \propton^{-1.74_{-0.07}^{+0.11}}$ and $\tilde{\mu}_{i,n} \propton^{-1.73_{-0.08}^{+0.09}}$, where $\tilde{\mu}_{e,n}$ and $\tilde{\mu}_{i,n}$are the medians of the eccentricity and inclination distributions. We also findthat intrinsic single planets have higher eccentricities ($\sigma_{e,1} \sim0.25$) than multi-planet systems, and that the trends with multiplicity appearin the observed distributions of period-normalized transit duration ratios. Weshow that the observed preferences for planet size orderings and uniformspacings are more extreme than what can be produced by the detection biases ofthe Kepler mission alone. Finally, we find that for systems with detectedtransiting planets between 5 and 10 days, there is another planet with agreater radial velocity signal $\simeq~53\%$ of the time.

Architectures of Exoplanetary Systems. III: Eccentricity and Mutual Inclination Distributions of AMD-stable Planetary Systems