In response to the comment signed "Uncle Al": I appreciate very much your criticism, whoever you may be, because it is a wonderful prompt to rephrase what I am trying to say and perhaps say it better.
What I am trying to say is what Werner Heisenberg expressed (loc. cit. 1962, 54) in this way: "The observation itself changes the probability function discontinuously; it selects of all possible events the actual one that has taken place. ... Therefore, the transition from the 'possible' to the 'actual' takes place during the act of observation." I take this statement to mean that, during a measurement act, a transition between two different modalities of being takes place, from a state of potentiality to a state of actuality. Thus, in the act of observation a state of potentiality ceases to exist. Since this is a necessary condition of all observations of potentiality states, it follows that such states are transempirical.
In the Double-Slit Single-Particle Interference experiments, specifically, we have to distinguish between the acts of observation or measurement, and the acts of labeling. A measurement act - that is, the act which leads to the actual appearance of a particle on a detector - is an irreversible interaction of a microphysical potentiality state with a macroscopic object or the environment. In contrast, the attachment of labels is not necessarily irreversible since labels can be erased.
Consider, for further clarification, the state of a single electron in a Double-Slit experiment immediately prior to its detection by a position sensitive detector, say a photodiode array. In this state the position of the electron across the detector does not have an actual value, but many potential values. I can describe this state somewhat figuratively by saying that a multiplicity of non-zero probabilities of being observed in different channels of the diode array is superimposed in it. More precisely, avoiding the term of superposition, I can use Villars' terminology and say that the electron is a "potentiality wave", that is, "a wave of potential observation interactions" (loc. cit. 1987, 148). When the measurement act is actually performed, one of the potential observation interactions contained in the potentiality wave becomes the actual one, i.e., the particle appears in a specific channel, and the potentiality state has ceased to exist. If it is felt that it is too casual to describe this event by saying that the observation has "destroyed" this state, I do not have to insist on this term. But, it is obvious, what is meant by it: during the act of observation a state of potentiality is terminated. When a state is terminated in the very act which is needed to observe it, it must be a transempirical state.
Please note, too, that the state of the electron immediately prior to detection in Double-Slit experiments can be of two types: it can define, as it were, an informed probability distribution; that is, the experiment was performed in such a way that it contains which-way information. Or the probability distribution is uninformed; that is, no which-way information is available. But it does not matter how the experiment was performed! In any case, observing a particle in one of the channels of the diode array means that a state of potentiality has ceased to exist, because the observation necessarily involves a transition from a state of potentiality to a state of actuality. These considerations show that Double-Slit experiments reveal a hidden order in two ways: 1) in the random appearance of single impacts on the detector; and 2) in the buildup of an interference pattern, if coherence is not excluded by the mode of the experiment.
Many other questions, suggestions, and details, which are per se very interesting, are listed in this response, but are irrelevant for my argument. Remember what the intent of my paper is: I want to explore whether the quantum phenomena can lead us to the notion of a domain of reality that transcends our experience. If one single instance can be found: that will settle the case. If not, we must conclude that the answer to my question is negative.