Manuscript XIV-G@1 · XIV-G.tex · input · 791c6644

Input statement: Tested-kernel equality and bound

G0: copied inputs and the unchanged stop › XIV-E: regrouping, root, and tested kernels · lines 480–500

XIV-G@1#input:Etested

For $G \in C_{c}^{\infty} (Z; Sym^{2} T^{*} M)$ ,

M_{ret} [G; h, ψ] = ⟨ L_{G} (a, b), h (a) ψ (b) ⟩ .

The kernel $L_{G}$ is the tested sum of $K_{4}, \dots, K_{9}$ , is compact, and satisfies

WF (L_{G}) \subset Z_{2}^{att} = {(a, ξ; b, η) : ξ + η = 0} ∖ 0.

“This is an intermediate attachment-kernel bound, not admission of the final quantum coefficient.”

“Nor does testing each fixed $G$ supply the uniform estimates needed to reconstruct a joint characteristic distribution in all four common variables” XIVE.

Displayed formulas in this passage

unlabeled · line 483
$M_{ret} [G; h, ψ] = ⟨ L_{G} (a, b), h (a) ψ (b) ⟩ .$
unlabeled · line 488
$WF (L_{G}) \subset Z_{2}^{att} = {(a, ξ; b, η) : ξ + η = 0} ∖ 0.$

Input statement: Tested-kernel equality and bound

Displayed formulas in this passage

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