Scope of the examples page: conditional computations, no experiment, and the deferred Bell-test destination

What the page contains. Three conditional computations in the declared framework: the worked comparison at the specified directions between the singlet arrangement and the EPR-type product mixture, with both CHSH values and an explicit local-response representation of the mixture (Worked Bell angles: the singlet against the EPR product mixture at the same directions); the finite-sample behaviour of the sample CHSH functional under a declared independent and identically distributed sampling model, with its concentration inequality and positive failure probabilities (Finite samples of a declared arrangement: the CHSH estimator, its concentration and the limits of a finite-sample verdict); and the selection and loss qualification, with the precise hypothesis under which the CHSH bound transfers to recorded pairs (Selection and loss: the precise hypothesis under which the CHSH bound transfers to recorded pairs).

What the page does not contain. No experiment item, no reported count, no calibration, no detector efficiency, no loss fraction, no background model, no trial-level uncertainty analysis, no p-value and no confidence level. The worked tables, the sample functional and the failure probabilities are probabilities of the declared models; no number on the page is an observation. The identification of any apparatus with the declared measurements and of any repetition procedure with the declared sampling model is a tested identification with uncertainty under P7 (Preparation and apparatus postulate P7: declared preparations, isolation and sampling assumptions).

Deferred Bell-test experiment destination. The design of the pair reserves an experiment item for a Bell test. It is not built here because none of the sources read for the pair supplies the required trial-level material: a primary or authoritative full report read directly, with the source-specific preparation and apparatus, calibration, measured outputs, trial count where reported, detection efficiency, losses and post-selection, background, the reported statistical treatment and systematics, and the source's omissions. The experimental remarks of the secondary sources — Binney's reference to the 1972 Freedman-Clauser test and its citation of a 1998 photonic test, and the MIT chapter's statement that experiments have confirmed violations — motivate the comparison only and are not used as measured records; no numerical value from them is reproduced. The statistics and primary-report gap named in the design is recorded as an open destination.

Why a null or shifted sample is not a verdict. The mixture's tables have $S=-\sqrt{2}$, so $\mathrm{\mid }S\mathrm{\mid }=\sqrt{2}$, strictly below the local-response CHSH bound $2$ (The CHSH bound for every binary correlation model admitting a local-response representation) and the singlet's $2\sqrt{2}$ (Worked Bell angles: the singlet against the EPR product mixture at the same directions). At the worked angles, every singlet table cell has probability $\frac{1}{4}(1\pm 1\mathrm{/}\sqrt{2})>0$, and every mixture table cell has probability either $\frac{1}{4}$ or $\frac{1}{4}(1\pm 1\mathrm{/}\sqrt{2})>0$; hence each finite sequence has positive probability under both specified independent-sampling models. Such a record cannot deductively exclude either member of this pair, though statistical evidence can favor one under an explicit comparison procedure and its assumptions. For a different specified pair, an observed sequence assigned probability zero by one ideal model can exclude that model conditional on its sampling assumptions. The worked comparison's spin calculations carry the Axiom of Countable Choice (The Axiom of Countable Choice (${\mathrm{A}\mathrm{C}}_{\omega }$)) and the Axiom of Choice (The Axiom of Choice) stated in their supplier hypotheses. The finite-sample analysis bounds the probability that the sample functional crosses a stated threshold under its declared model (Finite samples of a declared arrangement: the CHSH estimator, its concentration and the limits of a finite-sample verdict); it gives no universal impossibility result for all finite-sample comparisons. Any comparison also requires the preparation, detection, selection and sampling assumptions, and agreement is evidence about the combined assumptions, not a proof of the framework.

Model contrast is not an interpretation. The page compares the tables of two declared arrangements and the class of local-response models of those tables (The CHSH bound for every binary correlation model admitting a local-response representation); it makes no claim about the completeness of quantum mechanics, about hidden variables in general, about mechanisms or about any interpretation of the violation. The boundaries of the comparison are recorded on the pair's first page.