Nonexistence of weakly tight families at ${\aleph}_1<\mathfrak{s}=\mathfrak{c}=\aleph_2$

Let $\mathfrak{b}$, $\mathfrak{s}$, and $\mathfrak{c}$ denote the bounding number, splitting number, and continuum, respectively. A weakly tight family is the combinatorial object studied in the paper.

Nonexistence conjecture. There is a model of

$$\aleph_1=\mathfrak{b}<\mathfrak{s}=\aleph_2=\mathfrak{c}$$

in which there are no weakly tight families.

The conjecture concerns whether the separation $\mathfrak{b}<\mathfrak{s}$ can coexist with the nonexistence of weakly tight families in the specified cardinal configuration. The paper discusses related consistency results but does not establish this model, so the question remains open.