The injectivity conjecture for Tits homomorphisms

Let $M(\mathbf d)$ be a Coxeter monoid and let $\mathbf T_{\mathbf d}$ be a Tits homomorphism associated with it. Injectivity conjecture. All Tits homomorphisms $\mathbf T_{\mathbf d}$ are injective. This extends the Tits conjecture and its known generalization; the supplied status evidence indicates that this claim has been resolved.