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We constrain the intrinsic architecture of Kepler planetary systems bymodeling the observed multiplicities of the transiting planets (tranets) andtheir transit timing variations (TTVs). We robustly determine that the fractionof Sun-like stars with Kepler-like planets, $\eta_{\rm Kepler}$, is $30\pm3\%$.Here Kepler-like planets are planets that have radii $R_{\rm p} \gtrsimR_\oplus$ and orbital periods $P<400$~days. Our result thus significantlyrevises previous claims that more than 50\% of Sun-like stars have suchplanets. Combining with the average number of Kepler planets per star($\sim0.9$), we obtain that on average each planetary system has $3.0\pm0.3$planets within 400 days. We also find that the dispersion in orbitalinclinations of planets within a given planetary system, $\sigma_{i,k}$, is asteep function of its number of planets, $k$. This can be parameterized as$\sigma_{i,k}\propto k^\alpha$ and we find that $-4<\alpha<-2$ at 2-$\sigma$level. Such a distribution well describes the observed multiplicities of bothtranets and TTVs with no excess of single tranets. Therefore we do not findevidence supporting the so-called "Kepler dichotomy." Together with a previousstudy on orbital eccentricities, we now have a consistent picture: the fewerplanets in a system, the hotter it is dynamically. We discuss briefly possiblescenarios that lead to such a trend. Despite our Solar system not belonging tothe Kepler club, it is interesting to notice that the Solar system also hasthree planets within 400 days and that the inclination dispersion is similar toKepler systems of the same multiplicity.

About 30% of Sun-like Stars Have Kepler-like Planetary Systems: A Study of their Intrinsic Architecture