Manuscript I-B-VP-2@1 · I-B-VP-2-v1.tex · section · f4bd2b11

Finite records do not determine a wavefront

Supported laboratories, reporting, and non-transfer › Finite records do not determine a wavefront · lines 1761–1797

The finite supplied-report interface can install words describing

(α, β, bundle convention, formula, microlocal localization, status) .

For a calibrated clock basis, put

D_{j} = ⟨ τ_{j} ∣_{C} \otimes I_{A}, M (X) = j \sum ∣ j, w_{j} ⟩ ⟨ j, w_{j} ∣_{R} \otimes D_{j} X D_{j}^{†} .

Then

j \sum D_{j}^{†} D_{j} = I_{C A}, Tr_{R} M (X) = Tr_{C} X,

also with every untouched finite reference CheungIB,CheungEn09,CheungOOneST. The output contains $A$ , not a quantum return of $C$ . It reports installed descriptions; it does not acquire an unknown continuum wavefront set.

Finite linear tests do not determine a general distribution, and therefore do not determine its wavefront set. For example, for any fixed finite collection of tests one can choose more point-supported distributions than tests, at distinct regular points of a coordinate patch. Their evaluation map has a nonzero kernel. A nonzero combination in that kernel is singular but invisible to all the chosen tests. This is a coverage limitation in an unrestricted distribution class, not a construction of another Friedrichs covariance. The class-relative distinction is also emphasized in Oai282-A CheungOaiTwoEightTwo.

Displayed formulas in this passage

unlabeled · line 1764
$(α, β, bundle convention, formula, microlocal localization, status) .$
unlabeled · line 1769
$D_{j} = ⟨ τ_{j} ∣_{C} \otimes I_{A}, M (X) = j \sum ∣ j, w_{j} ⟩ ⟨ j, w_{j} ∣_{R} \otimes D_{j} X D_{j}^{†} .$
unlabeled · line 1775
$j \sum D_{j}^{†} D_{j} = I_{C A}, Tr_{R} M (X) = Tr_{C} X,$