The H-cobordism bound for Seifert fibered rational homology spheres

Let $M\to S^2$ be a Seifert fibered rational homology sphere with fiber multiplicities $d_1,\dots,d_k$. Seifert H-cobordism conjecture. If $M$ is rationally H-cobordant to zero, then

$$\sum_i\left(1-\frac{1}{d_i}\right)<3.$$

If $M=\Sigma(d_1,\dots,d_k)$ and $M$ is H-cobordant to zero, then $k\leq 3$. Known H-cobordant examples in the source have at most three singular fibers, but the conjecture is not resolved there.