Completeness conjecture for lens space knots in \Sigma$2,3,5$ and \Sigma$2,3,7$

Let $K_{p,k}$ and $K_{p',k}$ denote the parameterized dual knots in the tables for $\Sigma(2,3,5)$ and $\Sigma(2,3,7)$, respectively, and let $g(K)$ denote the knot genus. Completeness conjecture for the two tables. The table for $\Sigma(2,3,5)$ lists all $K_{p,k}$ in that homology sphere when $2g(K)<p+1$, and the table for $\Sigma(2,3,7)$ lists all $K_{p',k}$ in that homology sphere when $2g(K)>p'+1$. These assertions extend the proposed classification of the tabulated families; the source presents them as conjectures and gives no resolution.