Inequality conjecture for positive 2-bridge knot invariants

Let $K=C(p,q)$ be a positive 2-bridge knot with rational number $p/q$, where $p,q>20$. Let $v_3$, $a_2$, $a_4$, $\det(K)$, and $g$ denote the knot invariants used in the obstruction formula. Positive 2-bridge invariant inequality conjecture.

$$v_3\left(\frac{1}{2}\det(K)+3g-\frac{5}{2}\right)>7a_2^2-a_2-10a_4.$$

The conjectured inequality would imply that the obstruction formula cannot attain equality for these positive 2-bridge knots, supporting the broader claim that only the stated torus-knot exceptions admit chirally cosmetic surgeries. Its general validity remains open.