Manuscript X-A-conv-ST@1 · X-A-conv-ST.tex · proposition · 8ca47088

Proposition: No field-acquisition inference

Complete instruments for supplied evaluations › What the instrument does not acquire · lines 1703–1724 · proof included or linked

X-A-conv-ST@1#prop:noacquisition

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The instrument reports its installed finite input. It does not acquire $c_{ε}$ , $a (λ)$ , or a continuum gravitational observable.

Proof. For displayed numerical values $a_{j}$ , the report observable

B_{R} = j \sum a_{j} ∣ j, q_{j} ⟩ ⟨ j, q_{j} ∣_{R}

has pullback

M_{C}^{*} (B_{R} \otimes I_{A}) = j \sum a_{j} ∣ τ_{j} ⟩ ⟨ τ_{j} ∣_{C} \otimes I_{A} .

This is an observable of the supplied finite encoding. No map from unknown continuum field data to that encoding occurs in the input contract or Kraus operators.

Displayed formulas in this passage

unlabeled · line 1713
$B_{R} = j \sum a_{j} ∣ j, q_{j} ⟩ ⟨ j, q_{j} ∣_{R}$
unlabeled · line 1717
$M_{C}^{*} (B_{R} \otimes I_{A}) = j \sum a_{j} ∣ τ_{j} ⟩ ⟨ τ_{j} ∣_{C} \otimes I_{A} .$

Proposition: No field-acquisition inference

Displayed formulas in this passage

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