The remaining gravitational and diary obligations

The finite partner representation is not a relationally localized gravitational observable. The pair projector is not a freely falling detector coupling. Neither has a continuum short-distance structure.

Hadamard regularity, renormalized stress-energy, and detector response are separate objects in curved-spacetime quantum field theory Wald,SahlmannVerch,LoukoSatz. A state can satisfy named finite tests without those tests supplying a uniform bound on all unobserved degrees of freedom. Proposition prop:unobserved gives the elementary energy version of this warning.