Abstract

Landmark XI-C constructed a fixed-width classical graviton-tree symbol, not an admitted quantum insertion. We formulate the additional admission interface without replacing XI-B's finite-generator algebra by an unnamed Wick algebra. An essential distinction is made between exact off-shell representatives and classical symbols of an algebra that already imposes the free equations. Requiring the latter to reproduce every linear generator on all off-shell configurations is inconsistent.

A separate calculation decides a necessary condition for the proposed closure identity. The bare dressing ${\mathcal{B}}_f=-\int f{\mathsf{X}}_1[\gamma ]\cdot \partial \varphi$ has ghost number zero, but its free variation is generally nonzero. An explicit witness satisfies all the free multiplet equations and uses a ghost with admissible, unrestricted free Cauchy data. Consequently, for the observation tests in that witness, no admission respecting the classical free differential can make this bare insertion closed by adding only positive coupling-order corrections. The inherited second-order held-fixed-metric defect is also evaluated directly.

No quantum admission map is constructed, and no general nonexistence theorem for an appropriately formulated quantum extension is claimed. The overall ending is therefore Unresolved, with a proved conditional obstruction to the particular bare-insertion closure request. No antibracket, interacting differential, state, mixed loop, cubic Einstein contraction, or sharp-width limit is introduced.