The Norton–Sakuma classification conjecture for dihedral axial algebras

Let $A$ be a dihedral axial algebra of Monster type over a field of characteristic $0$. The nine Norton–Sakuma algebras are the nine classified dihedral algebras arising in this setting. Norton–Sakuma classification conjecture. The algebra $A$ is one of the nine Norton–Sakuma algebras. A version of this classification was already known under additional assumptions, including the existence of a Frobenius form; the paper notes that the form should not be required. A proof was announced by Franchi, Mainardis and Shpectorov in 2018, so the conjecture is treated as resolved.