Scope and empirical status of the page: what is adopted, what is proved, and what is excluded

The page works inside the framework's postulates P1, P2, P4 and P7 (State and composition postulate P1: Hilbert spaces, preparations and composite systems, Observable and probability postulate P2: self-adjoint observables, spectral probability and finite unsharp outcomes, Autonomous dynamics postulate P4: self-adjoint generators and unitary evolution, Preparation and apparatus postulate P7: declared preparations, isolation and sampling assumptions) and adopts, as additional model assumptions, the driven-dynamics reading of clause (iv) of P4 in The declared driven model: prescribed time-dependent energy families, propagator evolution and the two-level drive models: a prescribed time-dependent self-adjoint energy family in one of three regularity classes, carried by a unitary two-time propagator, with the evolved preparation and outcome-law readings and with the two declared two-level drive models of its clause (f). The interaction picture of the declared driven model: readings, the interaction propagator and picture equivalence of outcome laws fixes the interaction-picture readings, and The declared adiabatic protocol model: slow parameter, followed spectral subspace, uniform gap and leakage probability fixes the slow-family protocol, its followed spectral subspace and its leakage probability. All three are readings and model assumptions, not derived statements.

The bounded norm-continuous driven model: unique unitary propagator, Dyson truncation budget and outcome-law error proves well-posedness, the Dyson truncation budget and the outcome-law error in the bounded norm-continuous class; The bounded-control driven model: mild propagator, interaction-picture evolution and equivalence of the two readings proves the mild propagator and the equivalence of the Schroedinger and interaction readings in the bounded-control class; First-order transition amplitudes for a bounded control: Dyson remainder, the sinusoidal drive with its co- and counter-rotating parts, and the outcome-probability error proves the first-order amplitude with its explicit Dyson remainder and the closed sinusoidal drive with the co- and counter-rotating parts and the linear-in-time resonant growth; The common-domain driven model: strong propagator with domain invariance, and the driven oscillator as its declared instance proves the strong propagator and its domain invariance in the common-domain class and verifies the driven oscillator as an instance; The circularly driven two-level model: exact rotating-frame reduction, Rabi populations, resonance and inversion times proves the exact rotating-frame reduction and Rabi populations of the declared circular two-level model; The linearly driven two-level model: rotating-wave approximation with an explicit finite-time error contract and the averaged Rabi populations proves the rotating-wave error contract for the linearly polarized model with the bound on the population difference; and Finite-dimensional gapped protocol: the 1/T leakage estimate, the intertwining propagator and the Born leakage probability and The slowly varying one-centre Coulomb source: verified uniform gap of the n-th level and the 1/T leakage estimate prove the $1\mathrm{/}T$ leakage estimates in the finite and Coulomb-family branches. Every one of these is a conditional consequence of the adopted model data, the cited mathematics and P1, P2 and P4.

The page asserts no open-system or environment coupling, no non-unitary reduced dynamics, no thermalization or equilibration, no Fermi golden rule, no transition rate, no exponential decay, no resonance width, no spontaneous emission, no measurement or apparatus model and no branch selection by a ramping protocol; in particular the rotating-wave contract of The linearly driven two-level model: rotating-wave approximation with an explicit finite-time error contract and the averaged Rabi populations is linear in the elapsed time and gives no uniform-in-time approximation, the first-order amplitude theorem is a finite-time statement with an explicit remainder, and the adiabatic theorems are conditional on a uniform positive gap and coherent following. The uncompressed linear Stark coupling is not a bounded perturbation and does not appear.

The page records no experiment, no measured population, rate, frequency or lifetime, and no uncertainty record; its sources are mathematical and textbook treatments of the models, not experimental reports, so no measured value, no sampling model and no statistical inference enters any statement. The identification of a laboratory two-level system, spin, molecule or slowly varying source with the declared models and their parameters is a tested identification in the sense of P7 with its own uncertainty; agreement of a model computation with data would be evidence about the combined model and apparatus assumptions, not a proof of the framework.