Equality of density cardinals for singleton targets in the unit interval

For $r\in(0,1)$, let ${\mathfrak{dd}}_{\{r\},{\mathsf{all}}}$ denote the corresponding density cardinal; the same notation is used when ${\mathsf{all}}$ is replaced by $[0,1]$, $\{0,1\}$, or $(0,1)$. Singleton-target density-cardinal conjecture.

$${\mathfrak{dd}}_{\{r\},{\mathsf{all}}}={\mathfrak{dd}}_{\{1/2\},{\mathsf{all}}}$$

for all $r\in(0,1)$, and likewise for each of those replacements of ${\mathsf{all}}$. The paper notes that the equality is not known, although symmetry gives equality between the parameters $r$ and $1-r$; these cardinals can also be strictly smaller than ${\mathsf{non}}({\mathcal M})$.