Coincidence conjecture for admissible elements in $D^4$

Let $D^4$ be the object defined in the paper, and let $\alpha$ be an admissible sequence. Denote by $e_\alpha$ and $f_{\alpha 0}$, respectively, the corresponding elements of $D^4$, and by $\tilde e_\alpha$ and $\tilde f_{\alpha 0}$ their tilde counterparts.

Coincidence conjecture. For every admissible sequence $\alpha$, the elements $e_\alpha$ and $\tilde e_\alpha$, respectively $f_{\alpha 0}$ and $\tilde f_{\alpha 0}$, coincide in $D^4$.

The statement asserts that the two constructions of these elements agree for all admissible sequences. The supplied text gives no evidence about whether this claim has been resolved.