Theorem: L.4 summary

There exists a linear extension map ${\mathfrak{R}}_{\mathrm{L}}:{\mathcal{V}}_{\mathrm{adm}}\to {\mathcal{D}}^{\prime }({\mathbb{R}}^4)$ with ${\mathfrak{R}}_{\mathrm{L}}{|}_{{\mathcal{V}}_{\mathrm{K}}}={\mathfrak{R}}_{\mathrm{K}}$, built from the same $\varpi$-projections for $\rho \le 2$ and their extension to $\rho =3,4$, with zero declared moments (eq:L-moments), the scaling bounds of Proposition prop:RL(2), preservation of constant-coefficient relations, and the finite contact-defect ledger of Lemma lem:Ldefect. No root attachment, scale variation, or gravitational identification is constructed in L.4.

Proof. Definition def:RL and Proposition prop:RL; Lemma lem:Ldefect.