What the examples check, what they do not contain, and the empirical status of the companion page

Worked Rabi populations of the circularly driven two-level model: quarter-inversion, pi-pulse and detuned checks checks the exact Rabi populations of the declared circular two-level model at rational multiples of the Rabi period, including the quarter-inversion value $1\mathrm{/}2$, the pi-pulse value $1$, the return value $0$ and a detuned value $1\mathrm{/}4$; Worked rotating-wave error budget for the linearly driven two-level model: dimensionless instantiation and averaged Rabi check evaluates the rotating-wave error contract of The linearly driven two-level model: rotating-wave approximation with an explicit finite-time error contract and the averaged Rabi populations at declared dimensionless times, including one exact rational averaged population and the observation that the contract is conservative at the initial time; The two-level inversion model in an oscillating field: resonance, averaged Rabi inversion and its error contract matches the declared linear model onto an inversion-doublet family with an oscillating field, computes the averaged inversion probability and its pulse time and evaluates the error contract there for a declared coupling ratio; and The driven oscillator: exact classical response of a coherent preparation and stationary fluctuations checks the exact classical mean response and the stationary fluctuations of a coherent preparation of the driven oscillator of The common-domain driven model: strong propagator with domain invariance, and the driven oscillator as its declared instance clause (c).

The examples contain no measured frequency, energy, population, rate or lifetime; no apparatus, detector, calibration, sampling model or uncertainty record; no damping, relaxation, decoherence or environmental coupling; no identification of a laboratory spin, molecule, cavity or oscillator with the declared models or of a laboratory field with the declared drive parameters; and no claim that any declared parameter value is realized in nature. They also contain no Fermi golden rule, no continuum density of states and no long-time limit, in agreement with the scope of the companion A page (Scope and empirical status of the page: what is adopted, what is proved, and what is excluded).

All four examples are conditional computations inside declared models: their inputs are declared parameters, the cited mathematics and the postulates P1, P2 and P4. The sources cited are mathematical and textbook treatments, not experimental reports, so no empirical premise and no statistical inference enters any statement of the page. Comparing any of these model outputs with a laboratory oscillation or pulse would require a separately declared preparation and apparatus model with its own uncertainty and would test the combined model and apparatus assumptions; it is a tested identification in the sense of P7 (Preparation and apparatus postulate P7: declared preparations, isolation and sampling assumptions), not a consequence of the computations here.