Absolute-bound incoherence conjecture for equiangular lines

Let $\Omega$ be a set of $d(d+1)/2$ equiangular lines in $\mathbf{R}^d$. Here $\operatorname{Inc}(\Omega)$ denotes the maximum size of an incoherent subset of $\Omega$. Absolute-bound incoherence conjecture. Then

$$\operatorname{Inc}(\Omega)=d.$$

This would, together with the stated classification theorem, classify the sets of equiangular lines that saturate the absolute upper bound. Known nonexistence results rule out infinitely many feasible dimensions, but the conjecture remains open in general.