Cluster scattering diagrams via quiver moduli and tight gradings

We study rank‐2 cluster scattering diagrams through moduli spaces of quiver representations and a recently developed combinatorial framework of tight gradings. Combining quiver‐theoretic and combinatorial methods, we prove and extend a collection of conjectures posed by Elgin–Reading–Stella concerning the structural and enumerative properties of the wall‐function coefficients. The tight grading perspective also provides a new proof of the Weyl group symmetry of the scattering diagram.