Covariance and mixed kernel

In (eq:K), the infrared powers $P^{-1},P^{-2}$ are locally integrable in three momentum dimensions. The high-frequency terms are understood distributionally. The reflected term is retained. In particular, $H_{ww}=0$ is not the statement $K=0$.

These are prescribed chart comparisons. They are neither derived from the conical metric nor claimed to extend to a global conical two-point function. Functional Wick products and their domain restrictions are reviewed in FR.