Input statement: Tested kernels

For $G\in {C_c}^{\infty }(Z;{\mathrm{Sym}}^2{T}^{\ast }M)$, the residual-slot pairing gives an attachment kernel $L_G$ satisfying

It equals the tested sum of $K_4,\dots ,K_9$, is compact, and has

“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.