Constructing the conjectural toric Bridgeland stability condition

Prove that the subcategories of \(Nov\otimes_{Nov_+}\mathsf C_B\) defined by constructible metrized models with arbitrarily small reduced-singular-support phase amplitude form the slicing of a Bridgeland stability condition with central charge \(Z_\Omega\), and establish uniqueness of that stability condition.

Background

For the split symplectic torus, the paper constructs a large $Nov_+$-linear sheaf-theoretic category $\mathsf C_B$, reduced singular supports, and microlocal coefficient systems. It proposes to characterize semistable objects by the existence of constructible metrized models whose supports have phase amplitude arbitrarily close to zero. The conjecture asserts that these subcategories define, and uniquely determine, a Bridgeland stability condition after localization.