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Manuscript VI@1 · VI.tex · figure · b5b60afb

Switching-region audit

Sign, coefficient, and switching audit › Integration by parts changes a switched density · lines 2656–2675

VI@1#fig:VI-switching-audit

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metric / coordinatescalarswitching defectconditional quantumsupport / uncompleted
δ0V1m+δ1gS0m=−∫(∂μg)Tμνξν\delta_0 V_1^{\mathrm m}+\delta_1^g S_0^{\mathrm m}=-\int(\partial_\mu g)T^{\mu\nu}\xi_\nu
switching-region term
L~=L+∂μBμ\widetilde{\mathcal L}=\mathcal L+\partial_\mu B^\mu gives ∫gL~=∫gL−∫(∂μg)Bμ\int g\widetilde{\mathcal L}=\int g\mathcal L-\int(\partial_\mu g)B^\mu
discard a total derivative without the switch correction
(g−1)Xξϕ0=0(g-1)X_\xi\phi_0=0 near supp⁡f\operatorname{supp} f, yet the retarded switching term supplies the nonzero defect.

An observation plateau does not imply causal-region switch constancy. The Action Ward Identity is not a proved diffeomorphism Ward identity for this composite.

Switching-region audit. Compact switching produces explicit terms in the local Noether identity and when densities are changed by total derivatives. The plateau witness retains a retarded switching contribution even though the pointwise plateau term vanishes near the observation. These identities do not authorize dropping switching terms from a proposed quantum Ward identity.

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