Manuscript XIX-B@1 · XIX-B.tex · lemma · b5670709

Lemma: Formal-order separation

Observable comparison and the kernel boundary › Formal quantum order does not cancel the classical residual · lines 1375–1385 · proof included or linked

XIX-B@1#lem:hbar

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Let $E_{0} \neq = 0$ belong to a complex vector space $E$ . In $E [[ℏ]]$ , no correction in $ℏ E [[ℏ]]$ makes $E_{0}$ vanish.

Proof. The coefficient of $ℏ^{0}$ remains $E_{0}$ . Equality of formal series requires that coefficient to vanish.

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section: Formal quantum order does not cancel the classical residual