Debugging and quantifier audit

{@{}p{.34}p{.61}@{}} Potential error & Correct statement
Potential error & Correct statement

Declaring a third cone & The X-A-ST host, worldsheet, chart, signature ledger, and future relation are unchanged inputs.

Using conical global hyperbolicity & All Green operators, free fields, and causal support calculations belong to the Minkowski completion.

Counting the old first map again & Its formula is inherited. The new release consists of the second vertex and the iterated first vertex.

Adding a further copy of ${\rho }_{2,g}$ & The sum of the new pair already represents that one classical coefficient.

Using the positive Euler operator as the action Hessian & The Hessians are $-P_m$ and $-L_{j,g}$. The second-vertex response has sign $-L_{2,g}{\mathsf{E}}_{\mathrm{A}}$.

Ignoring $\partial g$ or its second derivatives & The operator and variation ledgers retain every switch derivative before imposing the plateau.

Applying iteration to an unspecified on-shell class & The intermediate expression $L_{1,g}{\mathsf{E}}_{\mathrm{A}}c$ is formed as an actual smooth compact test.

Inferring input descent from tree-exactness & Equation (eq:input-nondescent) shows that an equation-zero input can have nonzero response.

Interpreting the diagonal $R_2$ label as a hierarchy & It denotes a second Taylor coefficient of one quadratic first-vertex family only.

Using polarization to claim diagonal additivity & The cross terms in (eq:cross-terms) remain. No mixed hierarchy is installed by that identity.

Fixing a pair from normalization of its sum alone & Separate normalization or the stated recursion fixes the split.

Proving quantum uniqueness from only a classical limit & A formal-series uniqueness statement uses full coefficientwise normalization.

Calling sequential propagation a diagonal extension & Each Green operator acts on a smooth compact intermediate test. No Feynman square is assigned.

Treating a failed sufficient criterion as nonexistence & Only non-extension by the present tools is asserted, not universal failure of renormalized extensions.

Dropping the propagated first defect & The term $-L_{1,g}[h^{\prime }]{\mathsf{E}}_{\mathrm{A}}({\theta }_1-S_1{\mathsf{E}}_{\mathrm{A}}f)$ is part of (eq:var2).

Assuming $N_j$ or $g-\sigma$ has compact support & Only the defect combinations have compact generator support; no such global compactness is assumed.

Inferring off-shell equality from a quotient identity & The test difference is the explicit compact $P_m$-image in (eq:ideal-representative).

Using $k=0$ as a quadratic pure-gauge test & The correct two-jet includes $k=\frac{1}{2}{{\mathcal{L}}_{\xi }}^2\eta$.

Asserting a universal simple reversed-sign remainder & Sign reversal adds $2\mathbf{\varphi }(M{\mathsf{E}}_{\mathrm{A}}f)$; a $D{P}_m$-term cannot generally be dropped.