The embedding criterion for scalable spaces

Let $Y$ be a space, let $H^*(Y;\mathbb{R})$ denote its real cohomology algebra, and let $\bigwedge^*\mathbb{R}^N$ be the exterior algebra on a finite-dimensional real vector space. A space is formal when its rational homotopy type is determined by its cohomology algebra. The embedding criterion for scalability. A space is scalable if and only if it is formal and

$$H^*(Y;\mathbb{R})\text{ embeds in }\bigwedge^*\mathbb{R}^N$$

for some finite $N$. This is presented as a tempting conjectural extension of local cohomology-algebra embeddings; the supplied passage gives no resolution.