Abstract: I will discuss a valuative stability notion for fibrations, extending the one developed by Fujita and Li for Fano varieties and Dervan--Legendre for general polarised varieties, to the relative setting. The optimal symplectic connection equation is a canonical metric equation on fibrations, and I will also talk about how the valuative stability notion relates to this equation and to stability of fibrations. We expect it to play a similar role as the absolute notion does for K-stability and cscK metrics. I will also explain how valuative stability of the projectivisation of a vector bundle compares to slope stability of that vector bundle. This is joint work with Engberg.