Preparation and apparatus postulate P7: declared preparations, isolation and sampling assumptions

Adopt as physical assumptions of the framework the following discipline for comparing the model with recorded data.

(i) Declared model of each comparison. A comparison of a model prediction with an experiment of the framework requires, in addition to the state and dynamics assumptions P1-P5, the following declared items: a preparation model, that is, a specification of the state or preparation assigned to the system together with the physical procedure that realizes it; an isolation model, that is, the energy operator used and a statement of the interactions neglected in the approximation; a detection model, that is, the response of the apparatus, including efficiency, resolution, background and any binning; and sampling assumptions, that is, the statistical model under which repetitions of the preparation and detection are combined. None of these items is supplied by the mathematical framework alone.

(ii) Repetitions. The treatment of repeated trials as independent and identically distributed draws from the model's outcome law is an additional statistical model of the apparatus and the procedure. It is not a consequence of the state postulate and is not guaranteed by the mathematics; where it is assumed it is stated, and where it fails (correlated trials, drifting preparation, dead time, selection) the statistical analysis must model the departure or record the limitation.

(iii) Identification with uncertainty. The claim "this apparatus realizes the preparation $\rho$ and the dynamics $H_{\mathrm{o}\mathrm{p}}$" and the claim "this detector realizes the effect $F$" are physical identifications: they are tested against recorded behaviour of the apparatus, carry uncertainty and can fail. They are not derived from the framework, and a model prediction obtained under them inherits their qualifications. Calibration procedures, control experiments and their limitations are recorded with the comparison.

(iv) Empirical premises. Where a measured value enters a deduction - a mass, a charge, a field strength, a detector efficiency - it enters as a qualified empirical premise with its uncertainty, conditions of measurement and source, and the conclusion of the deduction carries those qualifications. A deduction that uses a measured input is not an exact statement about nature.

(v) Status. Clauses (i)-(iv) are adopted as the framework's conditions for comparing model with data. They make no claim that the framework or the apparatus description is exact; agreement of a prediction with a dataset is evidence about the combined model and apparatus assumptions, not a proof of the framework and not a statement about nature deduced from the mathematics.

• No sampling law from the state postulate. The probability law of P2 is a probability measure on outcomes of a declared measurement for a preparation; it is not by itself a probability distribution over finite datasets, which requires the sampling model of clause (ii).
• Records are classical. A detection record is a classical event with a time and a position in the arena, described by a classical apparatus trajectory; the model's outcome law assigns probabilities to records, and the recorded counts are compared with those probabilities.
• Qualification persists. Uncertainty and conditions carried by an empirical premise are not removed by exact subsequent algebra; the downstream conclusion inherits them.