Manuscript VII-A-ST@1 · VII-A-ST.tex · proposition · c39a67a3

Proposition: Equality under causal switch agreement

Causal support, switch equality, and classical comparison · lines 1277–1291 · proof included or linked

VII-A-ST@1#prop:cutoffequal

Fix $h, k, ϕ_{0}$ and the harmonic Cauchy prescription. If $g_{1} = g_{2}$ on a neighborhood of $D_{f}$ , then

O_{f} [g_{1}] = O_{f} [g_{2}] (mod κ^{3}) .

Proof. The scalar coefficient operators agree there, including their switch derivatives. Proposition prop:support gives identical scalar evaluations on $supp f$ . The coordinates do not depend on the switch.

Displayed formulas in this passage

unlabeled · line 1281
$O_{f} [g_{1}] = O_{f} [g_{2}] (mod κ^{3}) .$

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section: Causal support, switch equality, and classical comparison
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section: Causal support, switch equality, and classical comparison
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section: Causal support, switch equality, and classical comparison