  An elastic quartic twist theory has recently been proposed for chromonic
liquid crystals, intended to overcome the paradoxical conclusions encountered
by the classical Oseen-Frank theory when applied to droplets submerged in an
isotropic fluid environment. However, available experimental data for
chromonics confined to cylindrical cavities with degenerate planar anchoring on
their lateral boundary can be explained equally well by both competing
theories. This paper identifies a means to differentiate these theories both
qualitatively and quantitatively. They are shown to predict quite different
core defects for the twisted hedgehogs that chromonics generate when confined
to a fixed spherical cavity with homeotropic anchoring. In the quartic twist
theory, the defect core is estimated to be nearly one order of magnitude larger
(tens of microns) than in the other and, correspondingly, the director field
lines describe Archimedean spirals instead of logarithmic ones.
