Grothendieck-ring Verlinde relations conjecture for singlet modules

Let $\mathcal{M}(p_+,p_-)$ be the singlet vertex operator algebra, and let a suitable quotient category of its singlet modules have Grothendieck ring $K_0$. The relations obtained at the level of characters in the fusion-ring theorem and in the cited Verlinde-type construction are the relations under consideration. Grothendieck-ring Verlinde relations conjecture. These character-level relations remain valid inside $K_0$ of a suitable quotient category of $\mathcal{M}(p_+,p_-)$-singlet modules. The conjecture is motivated by the agreement between the character-theoretic Verlinde-type ring and the ring of regularised characters; the source gives this as evidence but does not prove the corresponding statement for the quotient category.