Status ledger and corrections

Free variation & Chain-rule formula proved with fixed preparation: Proposition prop:s0. Closure is not asserted.

Retarded interacting coefficient & Not assembled. Time-ordered normalization and the interacting identity remain unresolved.

BRST/BV observability & Not established. No interacting differential, Ward identity, or master construction is supplied.

Sharp-width and ultraviolet claims & Outside scope. No regulator-removal or all-orders theorem is performed.

The principal corrections to the original XVI-I are:

1. Admission implications are stated honestly. The additional $Z_3$ premise concerns the matching prepared kernel and implies narrow classical admission. It is not simultaneously imported and denied.

2. The ambient propagator is actually specified. Its translation-invariant definition is separated from a slab inverse. Algebraic inversion alone is not used as a wavefront theorem.

3. The two-edge recipe includes insertion derivatives. The source-delta derivatives and their signs are included in (eq:Vblock), not omitted from the power count.

4. Total derivative order is audited. The cubic Hessian places at most two derivatives in total on its two varied legs, not independently four. The insertion can add another two, yielding the conservative bound eight.

5. Nonvanishing has an off-diagonal test. The switch must be nonzero, and the derivative corrections vanish at the chosen jet. Scaling degree alone is not a nonvanishing proof.

6. Point and tangential ambiguities are separated. A finite point-extension family is not a classification of arbitrary tangential counterterms.

7. Root attachment is tested rather than merely withheld. The compressed product condition follows from the supplied root cone bound. The normalized coefficient nevertheless remains unselected.

8. Version references are synchronized. The current witness chain is not described using superseded XVI-E/F/G stops.