Manuscript XVI-B@1 · XVI-B.tex · section · 6a0abffd

Auxiliary evaluation and corrected support: XVI-F-v2

Update from the supplied later sheets › Auxiliary evaluation and corrected support: XVI-F-v2 · lines 1481–1512

Consequently, a representation

- \int K_{I}^{ab} (u) S_{λ, ab} (u) d u

with fixed smooth coefficients of this type has rapid decay by the same integration-by-parts proof as Proposition prop:root-decay. This is the direct fixed-data mechanism used for $I_{cand}$ in XVI-F-v2. It does not require transferring decay from $Q_{λ}$ .

XVI-F-v2 leaves the compatibility residual

Q_{λ} - I_{cand} = \int ρ^{ab} (u) S_{λ, ab} (u) d u

unresolved, with

ρ^{ab} (u) = \int_{R^{3}} a_{f, g} [ϕ]^{ab} (u, x) d^{3} x + K_{I}^{ab} (u) .

Its explicit advanced-field construction settles a spatial-integral identity for that constructed field. The remaining named check is its identification with the inherited advanced symbol on the boundary-flat source class.

The pairings are not proved equal and are not asserted to differ. Two rapidly decreasing scalar families need not be equal.

Displayed formulas in this passage

unlabeled · line 1484
$- \int K_{I}^{ab} (u) S_{λ, ab} (u) d u$
unlabeled · line 1495
$Q_{λ} - I_{cand} = \int ρ^{ab} (u) S_{λ, ab} (u) d u$
unlabeled · line 1500
$ρ^{ab} (u) = \int_{R^{3}} a_{f, g} [ϕ]^{ab} (u, x) d^{3} x + K_{I}^{ab} (u) .$

Auxiliary evaluation and corrected support: XVI-F-v2

Displayed formulas in this passage

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