In work of Haiden-Katzarkov-Konsevich-Pandit (HKKP), a canonical filtration, labeled by sequences of real numbers, of a semistable quiver representation or vector bundle on a curve is defined. The HKKP filtration is a purely algebraic object, yet it governs the asymptotic behaviour of a natural gradient flow on the space of metrics of the object.

In this talk, we show that the HKKP filtration can be recovered from the stack of semistable objects and a so called norm on graded points. This approach gives a generalisation of the HKKP filtration to other moduli problems of non-linear origin.