RemarkRemark: AI-adaptedProof: Not applicable

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Scope of the composites examples page: what the singlet, marker and mixture computations establish

Physical scope

A scope record for the examples page of the composites pair: the conditional computations it contains, their empirical status, and the content it does not supply. The record asserts no empirical result and no mathematical theorem.

Remarks

What the page contains. Three conditional computations in the declared framework: the singlet thought experiment of The spin singlet of two declared spin-half factors: directional correlations, perfect anti-correlation and setting-independent marginals with its reduced preparations, directional joint laws, correlation function and setting-independent marginals; the two-cell marked model of A two-cell marked model: the fringe visibility equals the marker overlap exactly, where the fringe visibility equals the marker overlap exactly and the theorem Marker overlap contracts the cross term: the detection law and the visibility bound of an overlap-normalized marked model is saturated; and the comparison of Improper and proper mixtures with the same reduced preparation: the singlet marginal versus a fair random mixture between the singlet's reduced preparation and a fair random mixture of factor preparations that assigns the same density operator. These computations retain the choice hypotheses stated by their suppliers, Countable Choice and (where a cited spectral PVM construction requires it) Choice (The Axiom of Countable Choice ( ${A C}_{ω}$ ), The Axiom of Choice).
What the page does not contain. No experiment, no reported count, no calibration, no efficiency, no sampling model, no statistical test and no measured correlation appears on the page; no item is a report of an observed outcome, and none of the computations establishes that the framework or any of its postulates describes nature. The model data of the marked example and of the singlet are declared idealizations; identifying a concrete apparatus with them is a tested identification with uncertainty under P7 (Preparation and apparatus postulate P7: declared preparations, isolation and sampling assumptions).
Statistics of the displayed probabilities. The detection weights and joint laws are probabilities assigned by the declared models to single-trial outcomes or phases. A correlation function is the expectation of a product of outcome labels computed from a joint law; it is not itself a probability. A finite sample of trials would require its own sampling model and would show fluctuations; no inference, error rate or conclusion is drawn here from the displayed numbers, and a measured fringe pattern would concern the accumulated distribution of many detections, not a single event.
Deferred comparisons. The Bell-type comparison of the singlet correlations with specified local-response models, with its angles, finite-data selection and loss caveats, belongs to the later Bell-models pair and is neither stated nor assumed here; nor does the page settle any interpretation of the alternatives, of the marker or of "which path", and it does not model any dynamical decoherence process.

Scope of the composites examples page: what the singlet, marker and mixture computations establish

Remarks

Depends on

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