Manuscript X-I-ST@1 · X-I-ST.tex · proposition · 9745fd40

Proposition: No acquisition conclusion

Complete destructive instruments and their composition › Why complete reports are not acquisition · lines 1868–1887 · proof included or linked

X-I-ST@1#prop:noacquisition

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The report instruments implement observables of the installed finite input, not measurements of an unknown continuum BV residual.

Proof. For a diagonal report observable $B_{R} = \sum_{j} b_{j} ∣ j, w_{j} ⟩ ⟨ j, w_{j} ∣$ , the pullback is

M^{*} (B_{R} \otimes I) = j \sum b_{j} ∣ τ_{j} ⟩ ⟨ τ_{j} ∣_{C} \otimes I .

It is an observable of the supplied clock encoding. No continuum-field input space or field-to-apparatus coupling appears in (eq:instrument). The same observation applies to (eq:numericinstrument).

Displayed formulas in this passage

unlabeled · line 1878
$M^{*} (B_{R} \otimes I) = j \sum b_{j} ∣ τ_{j} ⟩ ⟨ τ_{j} ∣_{C} \otimes I .$

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section: Why complete reports are not acquisition