Typical dense sets are strongly non-Rado in strictly convex Banach spaces with separable dual

Let $X$ be a strictly convex Banach space with separable dual. A typical countable dense set means a countable dense subset of $X$ in the sense used for typicality in the paper.

Strong non-Rado conjecture. Typical countable dense sets in $X$ are strongly non-Rado.

The paper establishes strong non-Rado behavior for a large class of reflexive spaces, while the corresponding classification for non-reflexive spaces is largely open. This conjecture proposes that strictly convex spaces with separable dual behave similarly to the reflexive cases.