Manuscript X-A-conv@1 · X-A-conv.tex · section · c76fffa3
Dependency audit
Controls, dependencies, and the exact release boundary › Dependency audit · lines 2162–2230
{}1.15
| Proved here | Assumed or frozen | Imported statement actually used |
|---|---|---|
| Regulated coefficient equations and uniqueness | Smooth off-shell configurations; fixed convolution and data | Standard smooth wave Cauchy theory and finite propagation BGP; the estimates used are recorded in Lemma lem:Cauchy. |
| Exact first-order regulator gap and positive smearing | The explicit | None. |
| Second-order bare coefficients and retained defects | Formal equality modulo | None. |
| Plateau scalar solution identity | The action-level switching in (eq:switchedaction) | VII-A is comparison only: its coordinates are unswitched. No theorem about the present regulator is imported. |
| Varied-action Noether identity | The curvature and density representative fixed here | None of the series intertwiners is used in this proof. |
| Off-shell domain and kernel continuity | Compact-open smooth topology and fixed-regulator kernel topology | VII-B and IX-A are comparison only. Neither supplies the topology or a product for this construction. |
| Coefficientwise non-repair statement | The first coefficient is held fixed | VI provides the comparison principle that different formal orders must not be conflated; the argument here is proved directly. |
| No quotient or representation conclusion | No on-shell or gauge-fixed quotient | III is used only to identify a different equation-space question. |
VII-C's hypotheses are not invoked or tested here. No sharp-limit argument is attempted. IX-E-2 and IX-E-3 supply no premise.