Non-left-orderability conjecture for involutory quandles of quasi-alternating links

Let $L$ be a quasi-alternating link, and let $IQ(L)$ denote its involutory quandle. A quandle is left-orderable if it admits a strict total order invariant under all left translations. Non-left-orderability conjecture. The involutory quandle $IQ(L)$ is not left-orderable. This conjecture extends the paper's non-left-orderability results for alternating links and several families of quasi-alternating links; it remains open for arbitrary quasi-alternating links.