Finite-vocabulary obstruction to elimination of imaginaries in Hrushovski constructions

Let $\tau$ be a finite relational vocabulary, and let $\boldsymbol{K}_0$ be the class of all finite $\tau$-structures satisfying the hereditarily positive $\epsilon$ dimension from Axiom 2. Let $\delta$ be Hrushovski's predimension, let $(A/B)$ be a good pair, and let $\operatorname{sdcl}^*(I)$ denote the symmetric definable closure modulo definable closure of proper subsets. Assume that there is a natural number $N$ such that

$$\mu(A/B)\geqslant\delta(B)$$

for every good pair $(A/B)$ with $\delta(B)\geqslant N$.

Finite-vocabulary conjecture. Under these assumptions,

$$\operatorname{sdcl}^*(I)=\emptyset$$

for every independent set $I$ with $|I|\geqslant\max\{N,5\}$. Consequently, no Hrushovski construction in a finite relational vocabulary $\tau$—that is, with $\boldsymbol{K}_0$ containing all finite $\tau$-structures—has elimination of imaginaries.

This is the source's exact formulation of the proposed sufficient condition. It would explain why the infinite-vocabulary construction can have elimination of imaginaries while finite relational vocabularies cannot; the source provides no resolution.