Theorem: L.6 summary

There exists a smooth family $\mu \mapsto {\mathfrak{R}}_{\mathrm{L},\mu }$ of coherent extensions of ${\mathcal{V}}_{\mathrm{adm}}$ with ${\mathfrak{R}}_{\mathrm{L},{\mu }_0}={\mathfrak{R}}_{\mathrm{L}}$, such that ${\mathfrak{R}}_{\mathrm{L},\mu }(u)-{\mathfrak{R}}_{\mathrm{L},{\mu }_0}(u)$ is supported at $0$ of contact order $\le N(u)$, the infinitesimal generator $A_{\mu }=\mu \mathrm{d}/\mathrm{d}\mu {\mathfrak{R}}_{\mathrm{L},\mu }$ exists and takes values in the same finite contact space, and every constant-coefficient relation in ${\mathcal{V}}_{\mathrm{adm}}$ is preserved. The construction is a scale-dependent subtraction prescription; it is not a physical gravitational beta function (Remark rem:Lscale). No explicit nonzero scaling residue (anomaly form) is claimed (Remark rem:Lressretch).

Proof. Definition def:RLmu; Proposition prop:RLmu0; Theorem thm:Lscale; Lemma lem:Ldiffmu; Remark rem:Lscale.