Miyaoka/Stark semistabil/Problem/en

Let

$Y\longrightarrow \operatorname {Spec} {\left(D\right)}$

denote a relative smooth projective curve over an onedimensional affine integral base of mixed characteristic (of finite type over ${}\mathbb {Z}$). Suppose that ${}{\mathcal {S}}$ is a vector bundle on ${}Y$ such that the generic bundle ${}{\mathcal {S}}_{\eta }$ over the generic curve ${}Y_{\eta }$ (in characteristic ${}0$) is semistable. Is it true that for infinitely many points ${}{\mathfrak {m}}\in \operatorname {Spec} {\left(D\right)}$ the bundle ${}{\mathcal {S}}_{\mathfrak {m}}$ over the curve ${}Y_{\mathfrak {m}}$ (in positive characteristic) is strongly semistable?