What the two-path detection page establishes, assumes and defers

What is established. The page declares the two-path preparation model The declared two-path preparation model and its ideal detection bins with its path components, coherent and which-path preparations and ideal detection bins, and the recorded detector and sampling model The declared recorded detector and sampling model of the two-path arrangement with its bounded effects, no-record channel, loss conditioning and declared independent trials. Coherent and which-path detection laws of the declared two-path model derives the normalized coherent bin law with its amplitude cross term, the which-path bin law, and the criterion under which the two declared laws coincide on every bin; the criterion comparing phase $0$ is conditional on the model being admissible at phase $0$. Recorded bin laws, loss and conditioning of the declared two-path detector derives the recorded-bin laws, the no-record mass and conditioned law, the reduction of indicator weights to ideal bins, and a sufficient condition for the recorded laws to coincide when the model is admissible at phase $0$. Continuity equation and local balance for the massive-model position density derives the continuity equation and local squared-amplitude balance for componentwise $C^1$-in-time, $C^2$-in-space solutions of the P4/P5 equation almost everywhere with the bounded measurable P5 potential. This density is a position probability density when the full-space state is normalized; under the theorem's domination and surface-flux hypotheses its finite total squared-amplitude integral is conserved on an interval. P4 separately gives norm conservation of the model's flow and total probability one for unit preparations. A finite sample can fail a criterion that rejects a positive-probability sequence shows that, within the declared independent-trials model, a declared fringe criterion that rejects a positive-probability outcome sequence fails with positive probability, and that no criterion distinguishes two recorded laws that coincide.

Adopted rather than derived. The path components, the relative phase, the preparation weight, the recorded weights and the independence of trials are declarations of the preparation and apparatus models in the sense of P7; the identification of a concrete arrangement with these declarations is a tested identification with uncertainty and can fail. The appearance of an interference pattern is not derived for any laboratory apparatus, and no count, efficiency, resolution, background or calibration value appears on this page.

Not claimed. The page does not assert which-path ontology, does not assign a trajectory to the particle between preparation and detection, and does not claim that the coherent preparation is the only admissible model of any apparatus. It makes no claim that a lower-dimensional screen is a spatial region of the model: a marginal, coarse-graining or flux reduction of a state to a screen coordinate or surface is a separate detection model. It also makes none of the following claims: that the flow of an arbitrary $L^2$ initial vector has a $C^2$ representative; that a recorded screen rate equals the surface flux; or that agreement of a finite dataset with a declared law establishes the framework.

Deferred content and destinations. Visibility loss by path marking and entanglement is not established here: the reusable marker-overlap physical result is homed on the entanglement page qm-composites-entanglement-and-reduced-states, and this page neither states nor consumes it. Photon polarization and optical interference are out of scope and belong to the photon and radiation page; the electron double-slit report is reported on the companion examples page, not here. Comparative classical field models and quantum-versus-classical model selection are likewise separate models.

Evidence status. The page contains no experiment and no measured value; the bounded, conditional statements above are consequences of the cited postulates, declarations and mathematics. The companion examples page reports one source-backed electron double-slit experiment with its disclosed limitations, and that report tests the combined model and apparatus assumptions rather than proving them.