Existence of bounded uniform stability segments

Let $X$ be a smooth projective variety, and let $\tau\in B(X)_{\mathbb Q}$. Let $\sigma'$ and $\sigma”$ be bounded stability parameters for the fixed topological type $\tau$. Uniform stability segment conjecture. Any two bounded stability parameters $\sigma'$ and $\sigma”$ can be joined by a bounded uniform stability segment. This would provide a general framework for connecting moduli spaces of Gieseker-semistable torsion-free sheaves through moduli spaces associated with bounded stability parameters; the paper proves the corresponding existence results for surfaces and for certain threefold wall crossings, while the general assertion remains open.