Critical-excess conjecture for distinguishable tree assignments

Let $H$ be a $k$-weakly-partition-connected hypergraph on $t$ vertices. A tree assignment of $H$ assigns a tree to every hyperedge occurrence, and the resulting labelled graph has a $k$-distinguishable tree assignment when its $k$-tree decomposition is uniquely determined by its signature.

Critical-excess conjecture. If

$$\sum_{e\in E(H)}(|e|-1)=k(t-1),$$

then $H$ has a $k$-distinguishable tree assignment.

This is presented as the natural repair of the refuted literal conjecture, after adding the missing critical-excess equality. The supplied text does not establish whether this repaired statement is proved or remains open.