Félix–Halperin–Thomas degree bound problem for rational Gottlieb elements

Let $X$ be a space such that $H^*(X;\mathbb{Q})$ is finite-dimensional, and let

$$N=\max\{n\mid H^n(X;\mathbb{Q})\neq 0\}.$$

The rational Gottlieb elements of $X$ are the elements associated to the rational Gottlieb group of $X$. Félix–Halperin–Thomas degree bound problem. The rational Gottlieb elements for $X$ are of degree less than $2N$.

The source presents this as an open problem concerning the location of odd-degree rational Gottlieb elements. Existing results give constraints for spaces of finite rational Lusternik–Schnirelmann category, but the stated degree bound remains open.