The expansion conjecture for finite topological rank

An $c9$-categorical structure is a structure whose theory has, up to isomorphism, a unique countable model. A structure admits a CIR when it has the property called CIR in the paper. Expansion conjecture. Any $c9$-categorical structure has an $c9$-categorical expansion which admits a CIR. This conjecture, together with the stated theorem that the absence of compact quotients implies finite generation and the example concerning compact quotients, would show that compact quotients are the only obstruction to finite topological rank. Its status is not resolved in the supplied text.