Manuscript IX-D@3 · IX-D-v3.tex · assumption · 3ad4586e

Assumption: Copied first-order switch witness

D6: the switch gate remains separate · lines 1528–1552

IX-D@3#ass:switch

Under the stated IX-A/VI switch-gap hypotheses, there is a compact gauge parameter $ξ$ , supported strictly after $Σ$ , with

L (K ξ) = ξ

and

B_{f} [h + K ξ, ϕ] - B_{f} [h, ϕ] = - \int f X_{ξ} ϕ .

For the specified switch and witness,

g K ξ = 0, a_{f} = \int f X_{ξ} ϕ \neq = 0.

The switched forced-response variation is zero, while the dressing variation is $- a_{f}$ .

These are copied witness hypotheses for the specified gauge and switch, not assertions about arbitrary switches or arbitrary gauge parameters.

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