A sectorial-projection criterion for weak unique continuation

Let $A$ be an elliptic differential operator of first order, and let $B_0$ denote the tangential operator associated with $A$ along a hypersurface. Write $P_+(B_0)$ for the positive sectorial projection of $B_0$.

Sectorial-projection criterion. There is a criterion for weak unique continuation for $A$ in terms of the range of $P_+(B_0)$.

The conjecture proposes replacing the symmetry assumption on the principal symbols of tangential operators by a weaker density condition on the ranges of the corresponding sectorial projections. The precise criterion is not given in the source.