Scoped companion comparisons

The following citations refer to source records, not new inputs. Where only a summary or excerpt is available, no independent verification of the complete companion proof is claimed.

strength and selected representations. Landmark II's finite certificate has a different object and domain from a quotient identity CheungII (statement :certificate). A finite fit is not automatically a global functional identity. No catalogue entry or target coefficient from II is a counterterm in this paper.

Landmark IV describes selected represented models, not a representation of every observable on the present quotients CheungIV (statement :model1). Gauge invariance is not prescription independence. Its representation parameter is not identified with the formal nilpotent $\kappa$.

-background currents, response, and higher jets. Landmark V uses the same sign identity and fixed-time response mechanism, but studies its own fixed-background metric functionals, compact representatives, and initial-surface terms CheungV (statements :gaugeidentity, :defect, and :rawclassification). It is not a replacement for the coupled quotient. The nonzero Ward pair here is neither the vanished exact repair nor a residual witness imported from V.

Landmark VI continues a coupled-coordinate construction to higher coefficients on a finite-time formal domain CheungVI (statements :descent and :gauge-action). Its transformations supported away from the initial surface are not identified with the whole group ${\mathcal{G}}_{\mathrm{R}}$. Neither result is a premise of the other, and neither constructs the sourced successor posed here.

VII-A's plateau-supported intertwining and larger-support defect belong to its switched model CheungVIIA (statement :plateau and corollary :nohigherrepair). The lower-order persistence principle is shared; the defect is not. That defect is not a failure of Theorem thm:retarded-section.

X-A's coordinate intertwiner retains equations, data, and switches CheungXA (statement :coordinate). Its complete first relational coefficient includes the switched scalar solution minus the coordinate dressing. The dressing alone is not a forced scalar correction, and X-A is not a repair of the Fourier regulator in this paper.

compatibility versus gauge-fixed solvability. XI-A records an empty invariant jet for a specified input and switched model, while XI-B explicitly retains gauge-fixed constructions without repairing that jet CheungXIA,CheungXIB. XII-C recomputes compatibility for a different selected action; XII-D constructs its corresponding forced response CheungXIIC (statement :empty) CheungXIID (statement :response). These records illustrate the distinction in Definition prop:three-successor.