Unresolved

Broad M-C (Definition def:MCcurv: proved functional matching plus an explicitly specified cutoff $\varpi$ and a functional representation of the entire collapsed scale variation): not achieved, because XVI-L leaves $\varpi$ unspecified (thm:L6). The top scale tensor has its own variational representative ${I^{\mathrm{top}}}_{\mathrm{scale}}$, so the M-C${}_{\mathrm{curv}}$ obstruction does not decide broad M-C; M-C${}_{\mathrm{data}}$ is satisfied. Their numerical values and the variationality of the resulting full tensor are not determined for the unspecified cutoff (Corollary cor:wpB-MC).

Lorentz covariance and variationality of the full (not only top) double-plateau scale tensor for the actual, unspecified $\varpi$.

The position-space identification of the predecessor $S$ at the origin $z=0$ ($S$ itself is globally defined, XVI-J; not needed for the punctured-space results).

Actual fixed-data dimensions where the actual ${\chi }_{\mathrm{I}}$ is non-constant, and transition regions (only $0\le \dim \ker {\mathrm{Collapse}}_{\mathrm{fixed}}\le 3321$); whether the actual ${\chi }_{\mathrm{I}}$ satisfies the hypotheses of Proposition prop:to-actual on given regions. Sufficient test (recorded in Section sec:to-timeonly): on an open $U$, a full-rank exact evaluation matrix of the joint family of external-data coefficient functions ${{\sigma }_{\epsilon }}^{(k)}(t){\partial }^{\rho }{\chi }_{\mathrm{I}}(x)$ occurring in the graph map, in ${\mathrm{Collapse}}_t$ and in the adjoint-defect map $H_t$; not verified for any concrete ${\chi }_{\mathrm{I}}$ (separate independence of the two factors does not suffice, Remark rem:to-joint).

Lower-order scale residues: their values depend on ${\nu }_k[\varpi ]$, $k=1,\dots ,4$; XVI-L does not fix $\varpi$; the radial comparison is a separately named specialization, not the XVI-L prescription.

Inhomogeneous ${\mathrm{Obs}}_L({\mathfrak{R}}_{\mathrm{L}})$ for a concrete $\varpi$ (M.7); the closed sector (M.8); restoration (M.9).

EOM and permitted field redefinitions for ledgers (3)–(4).

Powers of $\kappa$ and $\hslash$, the remaining factors of $i$, loop order, and the relation of ${\chi }_{\mathrm{I}}$ to the action weighting.

Physical (normalized) values of the matched coefficients.