Scope and empirical status of the light-matter and spectral-transitions page

What the page adopts. The page works inside the adopted radiation extension Radiation extension of the framework: transverse mode and photon assignments (a quantized free transverse sector with the mode assignments $\omega =c\mathrm{\mid }k\mathrm{\mid }$, $E=\mathrm{\hslash }\omega$ and $p=\mathrm{\hslash }k$, adopted rather than derived from Maxwell theory or special relativity) and the declared finite-level cutoff dipole model The declared finite-level matter model and its cutoff dipole coupling to the transverse radiation sector, whose matter factor is a declared finite-dimensional subspace of the two-body Coulomb relative-coordinate model with compressed dipole matrices and compressed Coulomb energy, and whose channel dipole coupling ${\eta }_0{\sum }_j{D}_j^{\mathrm{c}\mathrm{h}}\otimes \varphi (g_j)$ to a finite family of cutoff mode vectors, with declared real Cartesian channel weights, is declared model data. It also adopts the prescribed dipole-drive model The declared prescribed dipole-drive model and its long-wavelength regime with its long-wavelength regime, and the vacuum-preparation and quantized-field assumption The vacuum-preparation and quantized-field assumption for spontaneous emission in the cutoff dipole model. The identification of a laboratory system, field or apparatus with any of these models is a tested identification with uncertainty under P7 (Preparation and apparatus postulate P7: declared preparations, isolation and sampling assumptions).

What the page proves conditionally. The first-order emitted-photon energy law: factorised kernel, normalisation, concentration at the transition energy and positivity on positive-measure windows is the page's mathematics: the explicit factorisation of the single-vertex emission kernel, the normalised photon-energy law, its concentration at the transition energy for a continuous positive mode density, and the strict positivity of the law on windows of positive density. First-order emission and absorption amplitudes of the cutoff dipole model, and the exact model probability of the one-photon level-b projection up to the Dyson tail proves the single-vertex emission and absorption amplitudes of the model, the exact-model control of the one-photon level-$b$ projection probability by the explicit Dyson tail, and the exact mirror relation between emission into and absorption from a unit one-photon vector. The golden-rule limit of the single-vertex emission coefficient and its reading as a model rate coefficient proves the limit of the single-vertex coefficient per unit time and declares the model rate coefficient ${\mathrm{\Gamma }}_b=2\pi {\eta }_0^2{J}_b(\mathrm{\Delta })\mathrm{/}\mathrm{\hslash }$ under a continuous positive mode density, with the above-cutoff case tending to zero. Stimulated dipole-drive transitions of the finite-level model: first-order amplitudes, equal emission and absorption coefficients, and the exact two-level identification proves the first-order amplitudes of the prescribed classical drive, the equal stimulated emission and absorption coefficients for the same physical gap and prescribed real field, and the exact identification of declared two-level Pauli data with the circular and linear two-level drive models of the driven-dynamics page. Electric-dipole selection rules of the declared hydrogenic finite-level model: necessary angular conditions and the parity (Laporte) consequence proves the necessary angular and parity conditions on the uncompressed dipole matrix elements, and transfers their vanishing to compressed matrices when the declared finite-level subspace is spanned by a finite subfamily of bound states and its declared orthonormal basis is chosen from that same subfamily. All of these are conditional consequences of the cited postulates, mathematics and model data; their units are those of Dimensions, SI unit conventions and quantity types of the framework.

What the page does not claim. The page derives no Maxwell equation, no mode assignment, no Lorentz transformation law, no massless limit of the massive model and no coupling constant. It contains no experiment: there is no reported laboratory apparatus or preparation protocol, calibration, count, frequency, efficiency, background or uncertainty budget anywhere on the page, and none is invented. It asserts no measured spectral line, no measured rate, lifetime or linewidth, and no exponential decay law; the model rate coefficient of The golden-rule limit of the single-vertex emission coefficient and its reading as a model rate coefficient is a limit of an explicit model quantity, and its use as a decay constant over a time window would require additional adopted assumptions, as the sources record (Binney §9.3.1 on the continuum and long-time approximations; Box 9.2 on spontaneous emission as a zero-point-field mechanism added to the classical treatment). The page also does not claim that the coincidence of any model number with a measured ratio proves the framework, and it reports no statistical comparison: a comparison with data would test the combined model and apparatus assumptions, would require a declared sampling and measurement model, and would carry finite-sample fluctuations and systematic uncertainties.

Empirical status. An emission-spectrum or lifetime experiment is a candidate for a separate reported-experiment item, not a record of this page. Any such item would need an authoritative full report with the apparatus, preparation, calibration, measured outputs, trial counts where reported, resolution, background and the reported statistical analysis; sources that supply only historical line formulas or illustrative estimates do not authorize quantitative empirical claims. The relation of the adopted postulates and of the model's predictions to empirical support is recorded as a nonlogical support relation, not as a proof premise of any item on this page.