The Distribution of Planet Radius in Kepler Multiplanet Systems Depends on Gap Complexity

The distribution of small planet radius ($<$4 R$_\oplus$) is an indicator of the underlying processes governing planet formation and evolution. We investigate the correlation between the radius distribution of exoplanets in \textit{Kepler} multiplanet systems and the system-level complexity in orbital period spacing. Utilizing a sample of 234 planetary systems with three or more candidate planets orbiting FGK main-sequence stars, we measure the gap complexity ($C$) to characterize the regularity of planetary spacing and compare it with other measures of period spacing and spacing uniformity. We find that systems with higher gap complexity exhibit a distinct radius distribution compared to systems with lower gap complexity. Specifically, we find that the radius valley, which separates super-Earths and sub-Neptunes, is more pronounced in systems with lower gap complexity ($C$$<$0.165). Planets in high complexity systems ($C$$>$0.35) exhibit a lower frequency of sub-Earths (2.5 times less) and sub-Neptunes (1.3 times less) and a higher frequency of super-Earths (1.4 times more) than planets in low complexity systems. This may suggest that planetary systems with more irregular spacings are more likely to undergo dynamic interactions that influence planet scattering, composition, and atmospheric retention. The gap complexity metric proves to be a valuable tool in linking the orbital configurations of planets to their physical characteristics.