The analytic stability data conjecture for arbitrary central charges

Let $\Gamma$ be the lattice underlying $Vect_\Gamma$, let $Z:\Gamma\to\mathbb{C}$ be a central charge, and let $a(\gamma)$ denote the coefficients of rational stability data. For a ray $l$, write $C(l)$ for the associated strict convex cone.

Analytic stability data conjecture. The proposition asserting exponential bounds on $|a(\gamma)|$ for $\gamma\in C(l)$ holds for any central charge $Z$, not necessarily a rational one.

This extends the exponential-bound result from rational stability data to arbitrary central charges; the source states the extension without providing a proof.