The even-order M{"o}bius ladder local antimagic chromatic number conjecture

For $n\ge 2$, let $M_{2n}$ be the M{"o}bius ladder obtained from the cycle $C_{2n}=u_1u_2\cdots u_nv_1v_2\cdots v_nu_1$ by adding the edges $u_iv_i$ for $1\le i\le n$. Let $\chi_{la}$ denote the local antimagic chromatic number.

M{"o}bius ladder conjecture. For even $n\ge 4$,

$$\chi_{la}(M_{2n})=4.$$

The surrounding results establish the value for odd $n\ge 3$ and note that $M_4=K_4$ has local antimagic chromatic number $4$. The even-order case stated here is presented as a conjecture, with no resolution supplied in the text.