So state vector basis could be the map.

object is the territory.

But then to describe an object, using wave function or state vectors are more accurate than anything to describe the object. What if its the only way?

Lets take the case of time dilation in special relativity. Object doesn't time dilate directly but it is the result of speed and time and generally derived from the temporal part the lorentz transformation. Here:

lorentz transformation = map

object = territory

The best way to derive at time dilation is using the math of lorentz transformation and the observation is a result of geometry. There seems to be no other way to explain time dilation.

Right now. We describe objects and physics by means of math model. It is our only way to describe reality.

Therefore would it be wrong to say the basis in state vector where particle is described by it the only way how object arises (observable for example)? Then state vector is more fundamental.

Mathematically is there another way you can describe the basis and observable without using the concept of state vector basis or wave function? If there is none. Then the particle behaving or taking part in the dynamics of state vector and basis is the object itself. Here a basis can be considered as the property of an object. What if state vector and basis describing object is the true reality, then can't we say basis is a property of object and not just a choice humans make in the math for convenience?

Is there other things in physics where the choice humans make in the math for convenience is really what the objects are (isn't it Dirac Equation is like this, the math being the only way to describe the object and no other way, here the particle and dirac equation is the object itself. In this case perhaps one mustn't use the analogy of map and territory because it is a hybrid)).

In QFT, what does the basis stand for (if it is not observable in QM)?