Debugging audit

{@{}p{.36}p{.59}@{}} Potential overstatement & Correction proved or imposed here
Potential overstatement & Correction proved or imposed here

X-I-ST is the first classical interacting sheet & X-H-ST already has nonlinear classical kinematics and a relative interacting reference action. The new step is the compact order-three vertex.

An unspecified interaction is controlled & The profile, monomial, coupling order, ring, and finite reference coefficients are fixed explicitly.

The new interaction must alter the field BRST rules & A gauge-invariant leading scalar vertex can change Euler/antifield equations without changing field kinematics at the retained order.

Nilpotent field kinematics implies BV closure & The action identity and signed antifield lift are separately proved.

A third-order action needs only fourth-order geometry & The Einstein–Hilbert normalization requires the fifth geometric coefficient for the third action coefficient.

$\kappa =0$ removes an off-shell background tadpole & It does not. Equation (eq:tadpole) is retained. Full free BV equality is stated in the centered sector.

A positive-order truncation is an exact master action & The lift residual is explicitly nonzero at order four on the displayed evaluation.

Adding the volume density cancels every residual & The fixed-profile gradient remains in (eq:cutoffresidual).

The new residual is a universal completion obstruction & It is the residual of one named polynomial lift. A higher-order candidate changes it.

All residuals are one finite observable & Only a specified finite dictionary of real coefficient tasks is instrumented.

Odd residuals possess an intrinsic positivity order & Positivity is applied only after a specified real exterior-coefficient extraction.

A local action class can be arbitrarily weighted & A task names a representative or first passes to Euler expressions. Divergences are not silently reweighted.

Local functionals form an ordinary product algebra & Their ordinary products are included in the multilocal algebra.

Compact antighost, unrestricted auxiliary field & That domain need not be tangent to $s\bar{c}=b$. We use unrestricted germs, or compatible common support restrictions.

A compact ghost test is a nonzero free ghost solution & The two domains are distinct; compact spacetime homogeneous wave solutions vanish.

The reciprocity witness must vanish in any BV theory & The witness excludes an exact source-preserving identification, not every different variational action.

The witness is a loop anomaly & It is a classical ghost-number-zero pairing.

Preserving the three trees requires counting them again & The added interaction begins beyond their order. They are retained exactly once.