Debugging and quantifier audit

{@{}p{.34}p{.61}@{}} Potential error & Correction
Potential error & Correction

A second conical construction & The host is the already supplied X-A-ST instance. No cone, signature, or worldsheet is rederived.

Using global conical hyperbolicity & All global Green operators and free fields live on the declared Minkowski completion.

Treating split type as coordinate-free & The covector sum uses the fixed Minkowski affine identification only.

Equating joint admission and scalar-linear admission & The former tests polynomial background-slot kernels; the latter freezes backgrounds and admits smooth scalar tests. Neither quantizes $h,k$.

Using the positive Euler inverse as an action inverse & $S_0^{\prime \prime }=-P_m$, so the action retarded inverse is $-{\mathsf{E}}_{\mathrm{R}}$. The response test is $-L_{1,g}{\mathsf{E}}_{\mathrm{A}}c$.

Dropping $\partial g$ & The divergence-form operator explicitly contains $({\partial }_{\mu }g){a_1}^{\mu \nu }{\partial }_{\nu }$.

Applying $R_1$ to an unspecified on-shell class & The input is the supplied representative $F_c$. Equation-zero input representatives can have nonzero responses.

Putting $\hslash$ into the response test because of the CCR & The CCR belongs to the free product. The single contraction's $\hslash$ cancels exactly against the normalization factor.

Calling every object degree one & Only the retained response catalogue is degree one. The vertex and auxiliary verification have other field degrees, and instruments are channels.

A universal background degree-two claim & The degree bound applies to the retained list. Substituting background-dependent $c_2$ into the unweighted map can raise background degree.

Calling the mixed term positive & Its sign is $-\int fw\cdot \partial {\rho }_{1,g}$. The pure-gauge test verifies that sign.

Claiming a second-order identity from bare admission & The missing ${\rho }_{2,g}$ contribution is explicitly separated from the constructed truncation.

Inferring a nonzero total defect for every test from the coordinate edge integral & The edge and switch terms are separate. Smearing, equation-zero tests, and cancellations must be checked for each proposed total witness.

Using only $h=K\xi$ in a quadratic pure-gauge test & The complete $k=\frac{1}{2}{{\mathcal{L}}_{\xi }}^2\eta$ is retained.

Turning failure of a sufficient wavefront criterion into universal nonexistence & The theorem is non-extension by the present tools. No renormalized extension is ruled out universally.

Claiming every nonzero differential vertex necessarily has a nonzero uncancelled square obstruction & The universal endpoint operation fails its criterion; special numerators require separate analysis. No complete cancellation or noncancellation theorem is asserted.

Interpreting “no second pair” literally for every pair & The missing pair is the quadratic sector needed for a time-ordered family. Elementary linear products already exist in the free algebra.