The thin elements conjecture for formal globular and branching complexes

Let $\mathcal{C}$ be a strict non-contracting globular $\omega$-category. Let $C F^{gl}$ be its formal globular complex and $C F^{\pm}$ its formal branching and merging complexes, while $C R^{gl}$ and $C R^{\pm}$ are the corresponding reduced complexes. The formal thin elements conjecture. The folding operators of the globular nerve and of the branching/merging semi-cubical nerves induce quasi-isomorphisms

$$C F^{gl}(\mathcal{C})\rightarrow C R^{gl}(\mathcal{C})$$

and

$$C F^{\pm}(\mathcal{C})\rightarrow C R^{\pm}(\mathcal{C})$$

for any strict non-contracting globular $\omega$-category $\mathcal{C}$. The source notes that the folding operators are already known to be onto, and conjectures that they also induce quasi-isomorphisms; no resolution status is supplied.