No. If you have an empirical hard science, qi is a quantity measured by the investigator who is studying the behavior of the subject. The value of p is inferred from it in an empirically based model.
On the other hand, if you confound the model with that which is modeled, then qi=p by definition.
This is only handwaving unless you have actually measured p. For which of your models or demos have you measured p?
You can identify the controlled variable, p, the perceptual signal inside the subject, only inferentially. By the TCV you determine that your controlled variable p corresponds to the subject’s controlled variable p. In the TCV, you disturb your own perception from what you think is the subject’s reference value by means of your own outputs affecting a population of perceptible physical variables {v_1, v_2, ‥, v_n} which affect your intensity sensors, although typically you as investigator are controlling a higher-level perception originating in those intensity inputs; and you perceive and ideally measure outputs by the subject affecting that population of physical variables such that your controlled perception is restored to what you posited as the subject’s reference value for it. This is a very good empirical basis for the inference, but it is an inference nonetheless. What you have identified is your own perception of that population of perceptible physical variables {v_1, v_2, ‥, v_n} which you are both affecting. The TCV is a textbook case of the simplest form of collective control, conflict, gently initiated so that the subject can overcome it easily. It is the same, functionally, as letting the opponent win the tug of war or the arm wrestling. Two levels could model it.
But what you identify in physical fact is the population of perceptible physical variables {v_1, v_2, ‥, v_n} which affect your intensity sensors and the subject’s intensity sensors, and which are affected equally by your outputs and the subject’s outputs. This is what is called the CEV or CCEV, which you (as the investigator) demonstrate to be actually present in the environment precisely because both you and the subject are demonstratedly affecting it at the same time. This is a disciplined form of the social method by which living things test and demonstrate the reality of what they perceive to be real. It is the essence of scientific method, and the reason for publishing demonstrations which any properly trained colleague can replicate and possibly falsify. All of science is inferential, as any competent scientist will tell you. Engineers, medical practitioners, and non-scientists generally, require the findings of science to be authoritative. But I digress. I’m sure you know this. I want to avoid any appearance of demeaning your knowledge or intelligence.
The model is not that which is modeled. You are far from the only scientist who confounds the model with that which is modeled. For one critique, see
Lissack, M. R., & Richardson, K. A. (2001). When Modeling Social Systems, Models ≠ the Modeled: Reacting to Wolfram’s A New Kind of Science. Emergence, 3(4), 95–111. https://doi.org/10.1207/S15327000EM0304_7