Scope and empirical status of the three-dimensional scattering page

What the page establishes, and what it does not.

• Model deductions. The page proves, conditionally on the declared short-range model and the cited mathematics, the existence of the wave operators, their isometry and intertwining (Existence of the model's wave operators, isometry and intertwining, and the purely absolutely continuous free spectrum), the asymptotic completeness and unitarity of the scattering operator for the compact-support and resolvent-tail classes (Asymptotic completeness and the unitary scattering operator for real bounded compactly supported potentials, Asymptotic completeness for the resolvent-tail short-range class, with the decaying-tail example and the explicit exclusion of the Coulomb tail), the stationary outgoing solution with its amplitude and the cross-section readings (The model's stationary scattering wave, its outgoing amplitude and the differential and total cross-section readings), the controlled Born approximation with its operator-norm condition (The controlled Born reading: operator-norm condition, uniform amplitude error and coupling scaling), the phase-shift cross-section series (Partial-wave expansion, unit-modulus channel factors and the phase-shift cross-section series), the on-shell operator identification (Identification of the model's scattering operator with the on-shell stationary operator, and the central per-channel form), and the conditional resonance-model algebra (The resonance model's phase-shift law, unitarity and channel cross section). Every one of these is a logical consequence of the stated postulates, model declarations, hypotheses and mathematics; none of them is an observation.
• No observations. The page reports no experiment: it contains no apparatus, no calibration, no sample, no count, no uncertainty budget and no measured cross section. Nothing on the page should be read as a measurement of $V$, $\kappa$, a phase shift or a resonance parameter.
• What a comparison would require. To compare the model quantities $d\sigma \mathrm{/}d\mathrm{\Omega }$ or $\sigma$ with data one needs a declared target preparation (target density and composition), an incident fluence with its own uncertainty, a stated scattering geometry, a detector acceptance and efficiency model, and a background model, together with a declared statistical model for the counts. The equal-channel elastic flux assumptions of the beam model (The declared stationary elastic beam model: incident plane wave, scattered wave, current readings and differential and total cross sections clause (d)) must be justified for the particular apparatus; inelastic or multichannel processes lie outside the model and would require separate channels.
• Interpretation. Agreement of a measured count rate with the model reading is evidence for the combined model-plus-apparatus assumptions; it is not a deduction that the declared model, its potential class or the framework describes nature. Disagreement would not by itself falsify the whole framework, and a finite dataset can be compatible with a model without confirming it.

Scope of the model declarations. The potential is prescribed, not derived; the Coulomb coupling $\kappa$ and the resonance parameters $E_r,\mathrm{\Gamma }$ are model parameters, not measured constants; and the modified Dollard comparison of the Coulomb model is a declared construction whose phase convention changes only asymptotic channel phases (The declared long-range Coulomb model and its Dollard-modified free comparison clauses (c), (d)).