Density separation conjecture for polynomial Ramsey classes

For a family $\mathcal{F}$ of $3$-graphs, define

$$e(\mathcal{F})=\limsup_{H\in\mathcal{F}}\frac{e(H)}{\binom{v(H)}{3}}.$$

Let $\mathcal{F}_{\mathrm{poly}}$, $\mathcal{F}_{\mathrm{part\text{-}poly}}$, $\mathcal{F}_{\mathrm{polyfact}}$, and $\mathcal{F}_{\mathrm{part\text{-}polyfact}}$ be the graph families defined in the paper. Density separation conjecture.

$$e(\mathcal{F}_{\mathrm{poly}})<e(\mathcal{F}_{\mathrm{part\text{-}poly}})\quad\text{and}\quad e(\mathcal{F}_{\mathrm{polyfact}})<e(\mathcal{F}_{\mathrm{part\text{-}polyfact}}).$$

This conjecture predicts that allowing the relevant multipartite constructions strictly enlarges the attainable edge-density limits. The excerpt presents both inequalities as unresolved quantitative questions.