Zilber's theorem for continuous logic

Let $T$ be an $\aleph_0$-categorical $\aleph_0$-stable theory in a countable language, and let $T_P$ denote its expansion by a predicate $P$. The phrase arbitrarily small perturbations of the predicate $P$ refers to perturbing the predicate by an arbitrarily small amount in the relevant continuous-logic metric.

Zilber's theorem for continuous logic. Whenever $T$ is an $\aleph_0$-categorical $\aleph_0$-stable theory (in a countable language), $T_P$ is $\aleph_0$-categorical up to arbitrarily small perturbations of the predicate $P$.

This proposal concerns preservation of approximate $\aleph_0$-categoricity under the predicate expansion associated with beautiful pairs. The preceding construction shows the desired perturbation phenomenon in a specific Banach-lattice example, while the general assertion is left unresolved in the supplied text.