Evidence that Planets in the Radius Gap Do Not Resemble Their Neighbors
Planets in compact multi-transiting systems tend to exhibit self-similarity with their neighbors, a phenomenon commonly called ``peas-in-a-pod.'' Previous studies have identified that this self-similarity appears independently among super-Earths and sub-Neptunes orbiting the same star. Here we investigate whether this phenomenon holds for planets in the radius valley ($\sim 1.8\,R_\oplus$). Employing the \textit{Kepler} sample of planets in multi-transiting systems, we construct a difference-in-differences test comparing the observed fraction of size-similar adjacent pairs to the fraction expected from the underlying radius distribution alone, computed independently for valley-inclusive and valley-exclusive pairs. Non-valley pairs exhibit a $1.87\times$ enhancement of size-similar pairs above the baseline, consistent with the well-established peas-in-a-pod phenomenon. Pairs involving a radius valley planet show no such enhancement, and we exclude at $p = 0.001$ the hypothesis that the same size-similarity mechanism operates at the same strength for valley-inclusive pairs. The observed fraction of size-similar valley-inclusive pairs is consistent with independent draws from the radius distribution, with no additional intra-system correlation. We further compare the period ratio distributions for the two pair classes. While globally indistinguishable (KS $p = 0.848$), valley-inclusive pairs cluster near the 3:2 mean-motion resonance at more than twice the rate of the parent population, while avoiding the tightest orbital spacings entirely. The convergence of disrupted size-similarity and anomalous resonance architecture, together with independently measured elevated eccentricities among valley planets, is consistent with a stochastic process such as late-stage giant impacts contributing to the population of planets in the radius valley.