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 and empirical status of the composites page: adopted readings, derived results, and deferred content

Physical scope

A scope record for the composites, entanglement and reduced-states page: the adopted readings, the derived conditional results, the empirical status of the model computations, and the content deferred to later pages. The record asserts no empirical result and no mathematical theorem.

Remarks

Adopted readings. The page adopts the composition clause of P1 (State and composition postulate P1: Hilbert spaces, preparations and composite systems) for a declared pair of distinguishable subsystems, together with the observable and probability postulate P2 and the ideal conditional-measurement postulate P3 in the readings of Composite systems of the framework: product bases, local readouts, local effects and local instruments; the reduced preparations of Reduced preparations of a declared composite: the subsystem states of the framework; and, for the marked interference model, Declared marked two-component model: path components, marker states, phase family, detection weights and fringe visibility, whose path components, marker states and detector bin are declared apparatus data under P7 (Preparation and apparatus postulate P7: declared preparations, isolation and sampling assumptions). The composition assignment, the local readout convention and the marked model are adopted, not derived from the rest of the framework or from observation.
Derived results. The conditional results of the page are the Schmidt reduction, purity criterion and exact pure separability/product equivalence for pure preparations (Schmidt reduction of a pure composite preparation, purity of the subsystems, and the product criterion), the identification of local readout laws with the laws of the reduced preparation and its converse (Local readout laws and reduced preparations: the subsystem state determines, and is determined by, the local statistics), the invariance of the untouched factor's reduced preparation under discarded local instruments, with the conditional reductions averaging back to it (Local instruments and no-signalling: operations on one factor do not change the other factor's local statistics), and the contraction of the marker cross term with the visibility bound (Marker overlap contracts the cross term: the detection law and the visibility bound of an overlap-normalized marked model). Each is conditional on its stated hypotheses, including the choice hypotheses of the cited mathematics.
Empirical status. No item of the page reports an experiment, a count, a calibration or a measured correlation, and none is a proof about nature. The detection weights and the visibility of the marked model are probabilities and contrasts of a declared model; whether a concrete interferometer realizes a marked model with particular components, marker states and bin is a tested identification with uncertainty in the sense of clauses (i)-(iii) of P7, and a comparison of the model with recorded data would require the sampling, efficiency, resolution and background qualifications of the apparatus, which this page does not supply.
Localized detections and accumulated distributions. The detection weights of the page are probabilities for one trial of the declared model. An interference pattern is a property of the accumulated distribution of many detections, not of a single event, and a finite sample can fail a declared fringe criterion with positive probability under ordinary independent sampling even when the model is correct; nothing in the page draws a statistical conclusion from the displayed probabilities.
No-signalling is a model statement. The invariance proved in Local instruments and no-signalling: operations on one factor do not change the other factor's local statistics is a statement about declared local instruments of the adopted framework and its mathematics. It is not a relativistic causality principle, does not assert anything about spacelike separation, and does not by itself exclude alternative models; the conditional changes of the measured factor's partner are the correlations of the model, and every interpretation of the alternatives, of the marker and of "which path" is outside the page.
Deferred content. The following are outside this pair and are not supplied or assumed here: setting-independent local-response models and the classical-versus-quantum Bell comparison, with specified angles and finite-data caveats, which belong to the later Bell-models pair; a general theory of mixed-state separability, entanglement measures and separability criteria beyond the definition given in Product vectors, separable states and entangled states of a two-factor composite; the exchange sectors and exclusion statements for identical particles; quantum circuits, teleportation and computation; and any dynamics, interaction or open-system model of decoherence, the marked model of this page being a kinematic preparation model.

Scope and empirical status of the composites page: adopted readings, derived results, and deferred content

Remarks

Depends on

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