The conjectural vertex algebras for ind-constructible Calabi–Yau categories

Let $\mathcal{C}$ be an ind-constructible locally ind-Artin $3$-dimensional Calabi–Yau category endowed with a stability structure. Let a framing object be a chosen object used to define framed moduli and the associated representation-theoretic construction, and let a ray be a ray in

$$\mathbf{C}=\mathbf{R}^2.$$

The vertex-algebra existence conjecture. One can associate to $\mathcal{C}$ a class of vertex algebras parametrized by rays and by a choice of framing object; for almost all rays, the algebra is trivial. This is a proposed generalization of the toric Calabi–Yau construction from the paper's explicit examples to general three-dimensional Calabi–Yau categories, and the source gives no resolution.