Conjecture relating normalized single-hypergraph Turán densities across uniformities

For an integer $r\geq 2$, let $\Pi_{1}^{(r)}$ denote the set of Turán densities of single $r$-graphs. The normalized Turán-density conjecture. If

$$c\cdot\frac{r!}{r^r}$$

is in $\Pi_{1}^{(r)}$ for $r\geq 2$, then

$$c\cdot\frac{p!}{p^p}$$

is in $\Pi_{1}^{(p)}$ for every integer $p\geq r$. The conjecture is proposed as a mechanism that would imply the existence of an $r$-graph with irrational Turán density; the source does not state whether it has been resolved.