Scope of the Euclidean distribution-extension identity

Assume the Axiom of Choice (The Axiom of Choice) as in Exact four-dimensional Euclidean logarithmic scale anomaly. That proposition gives an exact Euclidean distribution-extension identity for the specified punctured kernel $u(x)=1\mathrm{/}(16{\pi }^4\mathrm{\mid }x{\mathrm{\mid }}^4)$: changing its cutoff scale changes the extension by $(8{\pi }^2{)}^{-1}\log (\mu \mathrm{/}\nu ){\delta }_0$. Its statement explicitly classifies it as a Euclidean distribution identity. By itself it does not say that an experimentally measured parameter changes with energy scale, choose which extension a physical model uses, or define a measurement procedure. It constructs no Lorentzian field theory. This remark asserts neither existence nor nonexistence of a field theory obtained by taking a continuum limit and supplies no empirical claim.