  The distribution of small planet radius ($<$4 R$_\oplus$) is an indicator of
the underlying processes governing planet formation and evolution. We
investigate the correlation between the radius distribution of exoplanets in
Kepler multiplanet systems and the system-level complexity in orbital period
spacing. Utilizing a sample of 234 planetary systems with three or more
candidate planets orbiting FGK main-sequence stars, we measure the gap
complexity ($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 physical characteristics of planets to their orbital
configurations.
