Periodic contact homology conjecture

Let $(Y,\xi)$ be a closed contact manifold with a periodic contact form $\alpha$. The closed Reeb orbits form components $S$ of the orbit orbifolds, and to each component associate the shifted graded filtered vector space $V(S):=H_{\bullet+\operatorname{gr}_S}(S;\mathbb{Q})$. Here $\operatorname{gr}_S=\operatorname{RS}(S)-\frac{1}{2}\operatorname{dim}(S)\mod 2$. Periodic contact homology conjecture. Then

$$CH(Y,\xi)\simeq \operatorname{Sym}\Big(\bigoplus_S V(S)\Big)$$

as filtered, graded vector spaces. The conjecture proposes a direct description of contact homology in the periodic setting; the source expects an $S^1$-localization proof using Pardon's formulation, but does not establish one.