Corrections and invariant safeguards

Existence versus an individual candidate. Vanishing of the obstruction means that some candidate descends. An individual candidate descends only if its own correction satisfies (eq:cancellation).

Complete module null test. The single identity $q{\delta }^{\prime }+\delta =0$ is supplemented by the complete coefficient criterion (eq:completekernel). Tangential distributional annihilators are retained.

Representative degree. Highest degree of a representative is not intrinsic. A possible quotient filtration is not excluded, but it is not identified with a representative-dependent leading term.

Relation classification. The universal/flat/jet distinction is stated for natural generator-compatible lifts. It is a filtration, not an asserted direct-sum classification, and a jet-visible relation need not have nonzero defect.

Point-puncture correction. The finite delta correction assumes an existing extension and applies to one point in the coefficient variables. It is not transported to the positive-dimensional graph locus without an additional theorem.

Flat multipliers. The correct counterexample uses ${b_3}^{\circ }$ with $v=e^{-2/x^2}$, yielding the nonextendable ${b_1}^{\circ }$. Multiplying ${b_1}^{\circ }$ by that same $v$ instead gives a smooth extendable function. Thus no blanket claim that flat multipliers never repair extension is made.

Support and ambiguity. The coefficient-extension theorem explicitly requires support on the response incidence. Its unrestricted ambiguity is not identified with the frozen partial-diagonal class. A normal-order bound alone does not bound tangential delta-derivative order.

Recovered definitions. The recovered $L$ relation, grouped cross-line pullback, characteristic locus, and partial-diagonal definition are recorded. Their availability is separated from implementation of the full graph operation.

Domain transport. No identity is transferred between distinct signatures or enlarged domains without explicit maps and domain inclusion. In particular, the canonical domain is not equated with the full characteristic complement.

Fixed normalization. The internal retarded pole and its delta part are unchanged. No characteristic coefficient adjustment, new regulator, selected finite part, or unfinished external limit is introduced.

Verification and attribution. The manuscript contains explicit proofs of its abstract claims. No successful compiler run, proof-assistant check, independent referee verification, or journal acceptance is asserted. Cheung manuscript references remain source-attributed manuscript citations rather than fabricated journal entries.