What the worked readouts of the companion page establish

Finite energy readout. An exact two-level energy readout and its moments computes, on the explicit two-dimensional state space, the spectral measure of the bounded observable $E_1{P}_1+E_2{P}_2$, the exact outcome probabilities of a pure and of a mixed preparation, and the mean, second moment and variance of the readout. The energies $E_1\mathrm{\ne }{E}_2$ are parameters of the assigned observable; the computation verifies the framework's law on finite data and asserts no apparatus realization, no measured level and no identification with a specific physical system.

Position bins. Position-bin probabilities of a Gaussian packet computes the first-coordinate law of a normalized Gaussian packet in the model's state space, its exact-value probability zero and explicit elementary bounds on the probability of a bin of positive length. The computation verifies the Born density reading of the model on a normalizable state; it reports no counts, no detector response and no resolution, and its bounds are mathematical estimates rather than uncertainty statements about an experiment.

Distribution caveats. The plane wave and the point-localized delta are not preparations of the model refutes the informal claim that a free plane wave or a point-localized delta symbol is a preparation of the model: both fail to be elements of the state space, and the model's exact-position statement is that the probability of an exact value is zero. The refutation concerns the state assignment; it does not deny the usefulness of these objects as distributional idealizations, and it makes no claim about approximation schemes in which they are formally employed.

Domains of the moment statements. A preparation with finite mean position and infinite variance exhibits a legitimate preparation whose position law has a finite mean and infinite second moment, so that the variance of the position law does not exist; the computation verifies that the domain hypotheses of the moment statements are genuine and not automatic. It asserts no measurement error, no disturbance and no apparatus behaviour.

Empirical neutrality. None of the four items is an experiment. Each is a finite or asymptotic computation inside the model's state space and outcome law, or a refutation of an informal claim about that model; none records data, calibration, sampling, uncertainty or a comparison with observation. Agreement or disagreement with data would test the combined model and apparatus assumptions and is not established or claimed here.