What the worked items of the companion page establish

Two-level precession. Precession of a two-level preparation: exact phases, probabilities and a Bloch-vector rotation computes, on the explicit two-dimensional state space, the spectral measure and flow of the assigned energy observable $E_1{T}_{u_1,u_1}+E_2{T}_{u_2,u_2}$ with $E_1\mathrm{\ne }{E}_2$, the exact phases of an evolved preparation, the outcome probabilities and expectations of three bounded observables, and the rotation of the expectation-value triple about the third axis with angular frequency $\omega =(E_2-E_1)\mathrm{/}\mathrm{\hslash }$. The computation verifies the flow and law of Assigned energy observable, unitary flow and the two pictures of autonomous evolution and Assigned sharp observables and the outcome law of the framework on finite data, and it confirms the energy conservation of Energy conservation, conserved sharp observables and the stationary eigenrays clause (a) in the model. No apparatus realization, detector resolution or measured frequency is asserted.

Finite superpositions. A finite superposition of energy eigenrays: exact phases, laws and return times computes the evolution of a nonzero finite superposition of orthogonal energy eigenrays, the trigonometric-polynomial form of the outcome laws of a bounded assigned sharp observable, the exact return-time criterion $({\lambda }_m-{\lambda }_n)T\mathrm{/}\mathrm{\hslash }\in 2\pi \mathbb{Z}$ for $m,n$ in the support of the coefficients, the existence criterion for a positive return time via a common frequency, and the two-energy specialization with least return time $2\pi \mathrm{\hslash }\mathrm{/}\mathrm{\mid }{\lambda }_1-{\lambda }_2\mathrm{\mid }$. These are exact model statements under the flow of The Schroedinger-picture flow: unitarity, domain invariance and the domain-qualified equation.

A failed universal claim. A superposition of distinct energy eigenrays need not be stationary refutes the informal universal statement that every superposition of energy eigenrays with distinct eigenvalues is stationary: on the two-level model with ${\psi }_0=(u_1+u_2)\mathrm{/}\sqrt{2}$ the outcome law of the flip observable takes the values $1$ at $t=0$ and $0$ at $t=\pi \mathrm{/}\mathrm{\mid }\omega \mathrm{\mid }$. The refutation isolates the relative phase as the mechanism and is consistent with the exact stationarity criterion of Energy conservation, conserved sharp observables and the stationary eigenrays clause (c): the individual eigenrays are stationary, while their equal-weight superposition is not when their eigenvalues differ. Distinct eigenrays with a common eigenvalue are not covered by this refutation: every nonzero superposition of their representatives is again an eigenvector with that eigenvalue and hence represents a stationary preparation, as in A finite superposition of energy eigenrays: exact phases, laws and return times clause (i).

None of the three items is an experiment: no counts, calibration, resolution, efficiency, background, uncertainty or data comparison appears anywhere on the page, and no energy value is measured. The two-level system is an abstract model and is not identified with a spin, a magnetic moment, a photon polarization or any other species; the coupling of spin to a magnetic field belongs to the corresponding model pages, and driven or resonant dynamics is deferred to the driven-dynamics development, which adopts its own time-dependent assumptions. The return-time and precession results are statements about the model's flow and outcome law, not about the stability, decoherence or control of any laboratory preparation.