What the worked instruments of the companion page establish

Serial filters. Serial ideal Stern-Gerlach filters: a two-level model computation computes, in a declared two-level spin-half model with the spin assignment of P6, the outcome probabilities ${\cos }^2(\theta \mathrm{/}2)$ and ${\cos }^2((\phi -\theta )\mathrm{/}2)$ of successive ideal filters and the quarter-probability case. The computation verifies the model's serial Lueders statistics for declared ideal filters. It does not derive the inhomogeneous-field force, the spatial splitting or the detector response of a Stern-Gerlach apparatus, and it reports no measured fraction and no property of silver atoms; the reported Stern-Gerlach experiments of 1922 remain a candidate experiment item that is not asserted by this page.

Analyser chain. Three ideal analysers in series: the quarter-intensity model computation computes the transmission probabilities of a chain of declared ideal analysers in a declared two-level model and exhibits the standard $\frac{1}{4}$ case, together with an explicit caveat that a stipulated classical amplitude model with the same ideal analyser convention gives the same ratio. The agreement of the two model computations does not establish field quantization or the applicability of either model to nature, and no transmission counts, efficiencies or backgrounds are reported.

Absorbing instrument. An absorbing two-outcome instrument: amplitude suppression and a branch without an outgoing polarization state exhibits a declared two-outcome instrument whose detected branch leaves an absorbed marker with no outgoing polarization-plane state and whose non-detection branch suppresses one amplitude by $\sqrt{1-p}$ rather than projecting it away; neither outcome is repeatable. The computation verifies that a declared instrument can describe a destructive apparatus within the framework's instrument vocabulary and that its update is part of its declaration. The three-level space is an idealisation; no real detector, photon number, efficiency or rate is described.

Degenerate readout versus fine readout. Coarse and fine declared measurements of a degenerate subspace: the Lueders update is not eigenvector selection contrasts a coarse readout of a degenerate subspace with a fine readout resolving it and shows that the coarse Lueders update retains the coherent superposition while the eigenvector-selection mixture changes the law of a suitable bounded observable. The computation verifies the degeneracy clause of the projective update inside an explicit three-level model; it asserts no preferred basis and no apparatus.

Empirical neutrality. None of the four items is an experiment. Each is a finite computation for a declared preparation and a declared measurement model; none records data, calibration, sampling, uncertainty or a comparison with observation, and none claims that a laboratory device realizes the declared instrument. Agreement or disagreement with data would test the combined model and apparatus assumptions under the preparation and apparatus postulate P7 (Preparation and apparatus postulate P7: declared preparations, isolation and sampling assumptions) and is not established or claimed here.