Distinctness conjecture for contact structures from Seifert surgery diagrams

Let $M$) be a Seifert fibered $3$--manifold described by Figure~, and let the diagram define contact structures by contact $(\pm 1)$--surgeries according to the stated algorithm. Assume the coefficients $r_i$ satisfy the conditions~. A contact structure is tight if it has no overtwisted disk.

Distinctness conjecture. All the tight contact structures defined by Figure~ and satisfying the assumptions~ are distinct up to isotopy.

The conjecture proposes that the surgery construction produces pairwise non-isotopic tight contact structures. The paper proves distinctness in the special family on $M(g,2g; (\alpha,1))$, while the general assertion is presented as a conjecture.