Uniaxial oblate-core conjecture for disclination lines

Let $c$ be the Landau–de Gennes tensor order parameter at a point on a disclination line, and let $s$ denote its scalar order parameter and $c{n}$ its director. Disclination-line core conjecture. For a point at disclination line, $c$ is always uniaxial, with $s<0$ (oblate) and $c{n}$ pointing in the axial direction. The source presents this as one of four conjectures about defect patterns, but supplies no further argument or resolution in the provided text.