Lamm's equivariant crossing number conjecture for two-bridge knots

Let $K$ be a two-bridge knot, and let $c(K)$ denote its crossing number. A symmetric diagram for a strongly invertible knot is a transvergent diagram whose axis is a straight line in the plane of the diagram and which is unchanged under a half-rotation about that axis. The equivariant crossing number $c_t(K)$ is the minimum crossing number among all symmetric diagrams for $K$. A continued fraction expansion $[a_1,\ldots,a_n]$ is of type (A) when all $a_i$ are positive, $n$ is even, and $a_2,a_4,\ldots,a_n$ are all even. It is of type (B) when all $a_i$ are positive, $n$ is odd, the integers are palindromic with $a_1=a_n,a_2=a_{n-1},\ldots$, and the central integer $a_{(n+1)/2}$ is odd.

Lamm's conjecture. $c_t(K)=c(K)$ if and only if $K$ can be represented by a continued fraction expansion $[a_1,\ldots,a_n]$ of type (A) or type (B).

The conjecture characterizes precisely when a two-bridge knot admits a symmetric diagram realizing its ordinary crossing number. The paper studies this question through the restricted invariant $c_2(K)$ and reports computations up to 14 crossings, but the conjecture is presented as an unresolved claim.