Unresolved

Explicit nonzero scaling residue (anomaly form) of $A_{\mu }(S^2)$ (Remark rem:Lressretch).

Answers to the matching questions (Q1)–(Q6) of Section sec:l8Q; any instance of L-D.

Nonvanishing of ${{\mathcal{C}}^{{\mathfrak{R}}_{\mathrm{L}}}}_{\mathrm{L}}$ after the switch ${\chi }_{\mathrm{I}}$ and the smearing.

The numerical value of ${{\mathcal{C}}^{{\mathfrak{R}}_{\mathrm{L}}}}_{\mathrm{L}}$ on explicit data.

Locality of the propagated ambiguity $\Delta {\mathcal{C}}_{\mathrm{L}}$ after propagation through $B_{f,g}$ (Remark rem:Lloc).

Whether the contact defects of Lemma lem:Ldefect are nonzero.

Lorentz covariance and the Leibniz (derivative-compatibility) property of ${\mathfrak{R}}_{\mathrm{L}}$.

The seminorm orders of the joint continuity statement in Theorem thm:Lmain.

BRST/BV compatibility of the completed graph (Remark rem:LBV).