Temporally pure properties

A temporally pure property of an object is an object whose possession by the object at a time is only a matter of how the object is at that time.

I don't know if there are any temporally pure monadic properties. Two kinds of candidates seems initially plausible: conscious mental properties like being in pain and geometrical properties like being round.

But neither kind of candidate seems to stand up to scrutiny. The shorter the amount of time a pain lasts, for a fixed intensity, the proportionately less one notices it. Therefore, if a pain were to last just for instant, one would not notice it at all—it would have zero temporal length. If this is right, then having a pain, and by extension having any other conscious state, cannot just be a matter of what happens at a particular time—it must be a matter of what happens at neighboring times. There is a supporting argument for this on naturalism: surely what mental states we have depends not just on the static properties of our parts, but also on dynamic ones, like the velocities of parts; but velocities are not a matter of what happens at any one time.

Geometrical properties, on the other hand, are surely relational. Being round seems to be a matter of the relations in which one stands to points in spacetime (on absolutist views of spacetime) or to other objects (on relational views). Moreover, three-dimensional shape is clearly relative to the reference frame.