Debugging and quantifier audit

{@{}p{.35}p{.60}@{}} Potential error & Correction
Potential error & Correction

Constructing a second cone & The I-B/X-A-ST host and chart remain unchanged.

Using global Cauchy theory on the regular product & All global analytical problems are on the declared Minkowski completion.

Calling the conical defect a worldline & It is the inherited worldsheet.

Swapping signatures in Euler equations & The host and analytical signature ledger is retained.

Using one Lie derivative on both sides of an Euler map & Input tensors and output tensor densities have the different Lie derivatives in (eq:types).

Dropping ${\mathcal{L}}_{\xi }{G}_{\mathrm{lin}}[r]$ & The exact F1 identity is used off shell.

Imposing $G_{\mathrm{lin}}[r]=0$ on every free graviton & The carrier equation is ${\mathsf{P}}_{\mathrm{gr}}r=0$; no strong de Donder constraint is added.

Deleting the linear kinetic equation in the background-field prescription & Only the fluctuation-independent Euler terms are removed.

Calling every retarded solution a variational Møller map & Proposition prop:nonvariational gives a concrete formal-adjoint obstruction to that unqualified claim.

Switching a source as though it were a density & Euler differentiation of a switched density produces additional onset derivatives.

Saying onset terms cannot affect a later observation & They can propagate. The direct variation instead uses compact generator support where $\sigma =1$.

Applying a retarded Green operator to an unprepared self source & The prescribed smooth onset is needed for the past-compact source domain.

Treating $N_0=D\circ {{\Delta }_{\mathrm{gr}}}^{\mathrm{R}}$ as globally compact & Its source argument can extend into the infinite past; $g{N}_0$, $\sigma N_0$, and generator-localized versions have the compact supports actually used.

Putting the first scalar argument only in $K_f$ & The $g{{\mathsf{E}}_{\mathsf{m}}}^{\mathrm{A}}f$ local terms extend it to $C$.

Putting every graviton contraction in ${\mathcal{D}}_C$ & A remaining graviton slot can range over $D_f$.

Equating a cubic kernel with a degree-one free class & The cubic is a distributional polynomial kernel. Only its appropriate smooth scalar contractions pass to $Q_m$.

Proving a two-point bound and omitting the cubic incidence & The diagonal source insertion and its normal covectors are included explicitly.

Adding a second ${\kappa }^2$ inside a tree coefficient & The three $T$'s are coefficients; the observable supplies one outer ${\kappa }^2$.

Applying the scalar response again to completed tests & The X-C-ST scalar pair is retained once.

Using a scalar equation ideal for a graviton remainder & Lemma lem:gslot supplies the graviton-slot membership actually required.

Inferring equation-ideal membership merely from free-shell vanishing & Only the forward implication is used; the needed preimage is exhibited.