Corollary: M-C curv obstructed; broad M-C not achieved

Assume Gate V. For the specified two-edge graph and the XVI-L prescription:

1. {M-C${}_{\mathrm{curv}}$} (Definition def:MCcurv) is Proved obstructed (graph-specific): for every $\mu$ and every admissible $\varpi$ the full collapsed scale variation does not lie in the span of the M.5 curvature targets, because its fixed $D=4$ component already lies outside.

2. Broad M-C is not achieved and remains Unresolved: criterion (i) of Definition def:MCcurv holds (the top scale tensor has its own variational representative ${I^{\mathrm{top}}}_{\mathrm{scale}}$, Theorem thm:wpB-dp(i)), but criterion (ii) fails because XVI-L leaves $\varpi$ unspecified (thm:L6). Their numerical values and the variationality of the resulting full tensor are not determined for the unspecified cutoff. {M-C${}_{\mathrm{data}}$} is satisfied.

This is not a claim about gravity generally. Adding non-gauge-invariant quadratic representatives to the ledger changes the target ledger of M-C${}_{\mathrm{curv}}$ but may remain within broad Target I; gauge-fixing/ghost or further graph contributions are another, independent enlargement.

Proof. (1) M-C${}_{\mathrm{curv}}$ requires a matching in the curvature-target span together with the matched-scale data of Definition def:MCcurv. The scale derivative equals the dilation defect at every grade ($B_{\mu }=0$; exact $\varpi$-independent top residues; Theorem thm:wpB-B0); the numerical values of the lower-degree components and the variationality of the resulting full tensor are not determined for the unspecified cutoff (XVI-L, thm:L6). But for every $\mu$ and every admissible $\varpi$ the collapsed scale tensor is not in the span of the ledger targets ($E_{P_1}$, $E_{P_2}$, $E_{\mathrm{EH}}$, $E_{R^2}$, $E_{{\mathrm{Ric}}^2}$, with the reading's weight): in the formal, $\chi$-plateau and preparation-plateau readings and in both time-only readings its $D=4$ component is not variational (table above; Corollary cor:wpB-timeonly), whereas every target is self-adjoint; in the double plateau its $D=4$ component is nonzero and outside $\mathrm{span}(E_{R^2},E_{{\mathrm{Ric}}^2})$ (Theorem thm:wpB-dp, Proposition prop:wpB-sep), and targets of degree $D=0,2$ cannot cancel it because collapse is homogeneous in $D$. The lower-order, $\varpi$-dependent part cannot repair this, for the same reason. (2) Theorem thm:wpB-dp(i),(ii): the $D=4$ component is the Euler tensor of ${I^{\mathrm{top}}}_{\mathrm{scale}}$, which lies outside the curvature ledger but is a local quadratic functional, so criterion (i) of broad M-C holds; criterion (ii) requires an explicitly specified $\varpi$ and a functional representation of the entire collapsed scale variation, which XVI-L, thm:L6, does not supply. M-C${}_{\mathrm{data}}$ (matching + explicit prescription-dependent scaling formulas) is satisfied.