Manuscript XIII-B@1 · XIII-B.tex · input · b8a5c0f5

Input statement: XIII-A's restriction release

B0: the inherited carrier and the restriction boundary · lines 307–335

XIII-B@1#input:restriction, XIII-B@1#eq:UCP

Fix a nonempty open $W$ with

W \subset P_{g} \cap {ε < t < T}, g_{W} = C_{c}^{\infty} (W; T M) .

The classical subclass is

C_{W} = {u \in C_{sol} : D^{*} b = 0 on W} .

Under the uniform support hypothesis

(UCP_{W}) g = 1 near J^{-} (supp f) \cap J^{+} (W) \cap M_{T},

the prescribed lift satisfies $Δ_{ξ} O ∣_{C_{W}} = 0$ for every $ξ \in g_{W}$ .

The coefficientwise vanishing space $N_{W}$ is not a two-sided ideal of the inherited product. Compact regular smearings give

[L_{q}, G_{h}]_{⋆_{H}} = i ℏ C (q, h) 1, C (q, h) > 0.

An admissible rank-one ordering change also fails to preserve coefficientwise vanishing on $C_{W}$ . No restricted quantum domain is handed off XIIIA.

Displayed formulas in this passage

XIII-B@1#eq:UCP · line 319
$(UCP_{W}) g = 1 near J^{-} (supp f) \cap J^{+} (W) \cap M_{T},$
unlabeled · line 310
$W \subset P_{g} \cap {ε < t < T}, g_{W} = C_{c}^{\infty} (W; T M) .$
unlabeled · line 315
$C_{W} = {u \in C_{sol} : D^{*} b = 0 on W} .$
unlabeled · line 329
$[L_{q}, G_{h}]_{⋆_{H}} = i ℏ C (q, h) 1, C (q, h) > 0.$

Input statement: XIII-A's restriction release

Displayed formulas in this passage

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