Jacobsson's conjecture on the lower grading of Gottlieb elements

Let $X$ be a formal space with bigraded Sullivan minimal model $(\land V,d)$, where

$$V=\bigoplus_{i\geq 0}V_i$$

and the differential satisfies $d(V_0)=0$ and $d(V_i)\subseteq (\land V)_{i-1}$ for $i\geq 1$. A Gottlieb element is an element of the model corresponding to a rational Gottlieb element of $X$. Jacobsson's conjecture. All Gottlieb elements are contained in

$$V_0\oplus V_1.$$

This conjecture concerns the location of Gottlieb elements in the bigraded minimal model of a formal space. The even-degree case is proved in the paper, while the general assertion is not established here.