Generic finite-parameter families of smooth vector fields have finiteness properties

Let $Vect^*\,S^2$ be the set of all smooth vector fields on $S^2$ with isolated singular points satisfying a Łojasiewicz inequality and with finitely many cycles. A smooth vector field belongs to $Vect^*\,S^2$ if it has these properties.

Generic-family conjecture. Smooth vector fields met in a generic finite-parameter family belong to $Vect^*\,S^2$.

This asserts that generic finite-parameter families avoid smooth vector fields with nonisolated singularities, without the stated Łojasiewicz finiteness property, or with infinitely many cycles. The supplied text gives no resolution status or further context, so the conjecture is recorded as open.