Who defines the preset sound at MIDI velocity 64? ...

Velocity is guided by mechanics rather than tone. In Pianoteq, this would be the momentum with which the hammer hits the simulated strings. In sampled VIs, this would be the strength with which a key is hit (VSL use a "robot finger" to make it repeatable).

So, if different instruments sound different at the same velocity, that would be a fair reflection of the playing experience on different instruments: variable outcomes for the same input.

The editorial choice that a human would make would be to define the maximum force for vel=127 (as well as the minimal for vel=0, as I imagine we wouldn't start from nothing). I would speculate in pianoteq this choice is consistent within instrument groups (ie. obviously a different choice between the steinway and a steel drum).

So vel=64 falls out of the wash.

Is Pianoteq using a "robot finger" too since day one?
With 127 fixed mechanical velocities to sample the original pianos and then design a physical model of the same loudness and sound dynamics?

If so, the mechanical velocity 64 is fixed since the beginning and the physical model would not make a difference if two original pianos have a different dynamic response.

I know that Pianoteq is not a sampler. But don't they use samples for orientation that the physical model is similar to the original piano?

Not important for this thread, but my opinion is, that 127 levels are good-enough, yes, ... but only if the distribution/mapping to mechanical levels is well done. Where many controllers fail. Who or what determines, how a pianoteq piano preset should sound at vel 64, if not a (algorithmic) "robot finger"?

So you vote for algorithm? ->
Quietest note of the original piano is defined as velocity 2 and loudest as velocity 127. The other volumes are generated by a term similar to D  x ([log (velocity) / log(127))

An iterative process is possible, which means there is a human factor /arbitrariness  in the velocity response of each instrument preset. Then it is unlikely, that a one-fits-all, global velocity curve for an individual midi controller exists.

Isn't it human to assume that the middle velocity level is associated with the medium / standard / basic response of a virtual instrument? It wouldn't be rationale to think, that the medium response per design is chosen at low vel 32 or  high vel 96 for example. But if humans are iterating it can happen, that one designer balances the medium response of a preset at 61 and the other at 66. Change your preferred velocity curve at mezzo-forte in this magnitude and a preset feels and sounds significantly different.

I have a steep hypothesis at the moment, that a physical background determines the mezzo-forte range of a midi controller:

It is at the point, where the key accelerates with 1G (= 9.81 m/s²)

Why? Based on the graph that has been mentioned in a parallel thread recently:

It seems that the muscle memory "feels" when the hand is accelerated with more than 1G (mf to fff) and slowed down with less than 1G (mp to ppp). From the graph I learned, that with a weight of >=500 g a key acceleration of 1G is reached with a common action. It might be more than a coincidence, that I had calibrated my velocity map just by ear and trial & error to vel 72 at mezzoforte (64) long before. Practically the same velocity ~70 that my midi controller outputs at 1G under factory-defaults.

With this hypothesis the mezzoforte point (64) in the velocity curve can be mapped to the midi velocity at 1G (in this example 70 -> 64). The pianoteq calibration assistant calls this center point "normal touch, neither light nor strong" / "intermediate velocity".

But this is just one fixpoint of five used by the calibration assistant. Would be nice to deduce the other four points of the curve similarly, they seem to be less determined. For the lowest (controllable) velocity, I have chosen the point, where the rubberdome contact collapses under a static weight (can be felt with the fingertip, a bit like fake-let-off). With 100 g the rubber dome holds the weight, with 125 g it collapses (I don't take smaller intervals than 25 g for efficiency).
So I define that calibration point with 125 g.

A higher grade of arbitrariness has the calibration point "low velocity" "light, piano, touch". Between 125 g and 500 g I have chosen 250 g for this calibration point. It is in between the former values (of course) and the half of 500 g. And 125 g is the half of 250 g. I hope for some hidden math, that it makes some sense ;-), at least it provides a very similar value like my old trial & error curve.

The fff mapping is relatively uncomplicated, because my controller seems to be limited somewhere at 105.

You may ask at this point, where is calibration point 4, the forte f mapping? I have no idea at the moment, how to map this point other than trial & error ...