Katada's stable Albanese cohomology conjecture for IA_n

Let $H(n):=H_1(F_n,\mathbb{Q})$ and $H^\vee(n):=H^1(F_n,\mathbb{Q})$. Let $H_A^*(\operatorname{IA}_n,\mathbb{Q})$ denote the image of the cup-product map from the exterior algebra on $H^1(\operatorname{IA}_n,\mathbb{Q})$ to $H^*(\operatorname{IA}_n,\mathbb{Q})$. For $n\gg *$, let $\mathsf{IH}$ be the ideal generated by the displayed relations, where $\{e_1,\ldots,e_n\}$ is the standard basis of $H(n)$, $e_i=[x_i]$, and $\{e_1^\#,\ldots,e_n^\#\}$ is the dual basis. For $f_1,f_2,f_3\in H^\vee(n)$ and $v\in H(n)$, the generators have the form

$$\sum_{i=1}^n (f_1\wedge f_2\otimes e_i)\wedge(e_i^\#\wedge f_3\otimes v)-(f_3\wedge f_1\otimes e_i)\wedge(e_i^\#\wedge f_2\otimes v).$$

Katada's conjecture. For $n\gg *$,

$$H_A^*(\operatorname{IA}_n,\mathbb{Q})\cong \frac{\bigwedge^*(\bigwedge^2 H^\vee(n)\otimes H(n))}{\mathsf{IH}}.$$

The conjecture is a proposed complete description of the stable Albanese cohomology of $\operatorname{IA}_n$, based on calculations in low degrees. The source records no proof or disproof of this statement.