Six-pattern conjecture for lens surgeries on the Poincare homology sphere

Let $\Sigma(2,3,5)$ be the Poincare homology sphere, let $K\subset\Sigma(2,3,5)$ be a knot, and suppose

$$L(p,q)=\Sigma(2,3,5)_p(K).$$

For $h\in\mathcal{H}(p,K)$, where $\mathcal{H}(p,K)$ is the set defined in the source, six-pattern conjecture. Either one of the following six patterns holds:

1. $L(p,q)=L(54\ell^2+15\ell+1,27\ell^2+21\ell+3)$ for $\ell\in\mathbb{Z}\setminus\{0\}$;
2. $L(p,q)=L(54\ell^2+39\ell+7,27\ell^2+33\ell+9)$ for $\ell\in\mathbb{Z}\setminus\{0\}$;
3. $L(p,q)=L(69\ell^2+17\ell+1,46\ell^2+19\ell+2)$ for $\ell\in\mathbb{Z}\setminus\{0\}$;
4. $L(p,q)=L(69\ell^2+29\ell+3,46\ell^2+27\ell+4)$ for $\ell\in\mathbb{Z}\setminus\{0\}$;
5. $3.21\leq h^2/p\leq 3.61$;
6. $1.15\leq h^2/p\leq 1.28$.

This is a rough conjecture based on the plotted data for lens surgeries on the Poincare homology sphere. The source does not establish the conjecture or provide a resolution status.