Sign-coherence conjecture for the rows of $H^v$

For each vertex $v\in\mathrm{Ex}_0(B)$, let $H^v$ be the associated matrix. A collection of entries is sign-coherent when, in each coordinate, the relevant entries are all nonnegative or all nonpositive. Sign-coherence conjecture for the rows of $H^v$. For each vertex $v\in\mathrm{Ex}_0(B)$, the rows of $H^v$ are sign-coherent. The source presents this as an equivalent formulation of the constant-term conjecture and gives no general resolution.