Manuscript IX-B@2 · IX-B-v2.tex · section · 8ce915d6
Dependency ledger
Dependency ledger · lines 483–577
ledger
The source labels below refer to the delivered manuscript versions. The last column gives the local point of use. Inherited existence, topology, and ultraviolet statements are not promoted to new product theorems.
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| Source | Inherited statement | Local use |
|---|---|---|
| VII-C | Tensor cancellation gives ; the mixed covariance retains its reflected branch (prop:tensor, eq:K). | (eq:tensor), (eq:K) |
The logarithmic coefficient is the light-ray number , positive for separated tests (thm:log, lem:separated). | (eq:C); Theorem thm:diagonal | |
Normal kernel convergence and divergent unchanged coefficients exclude the coefficient extension and the algebra under (E1)–(E4) (lem:normalconv, thm:coefficient, ass:extension, cor:noalgebra). | Section sec:continuity | |
| Observation-diagonal subtraction is insufficient. Subtraction on old regular products changes those products; a sharp-only assignment does not restore continuity (Section “Counterterms and the scope of the conclusion”). | Theorem thm:diagonal; Remark rem:subtraction | |
| VII-D | The prescribed placement yields the smooth family (sc:placement, prop:positive). | (eq:T), (eq:G) |
The residue is ; its product pairing equals . The local chart has no (def:residue, prop:ledger, eq:rlocal). | (eq:r), (eq:C), (eq:density) | |
The strong finite part has order- control, including the reflected-diagonal intersection; complete parent conversion is (thm:finitepart, thm:conversion). | Assumption ass:VIID | |
| Parent adjoint symmetry, cocycle, and scale dependence are fixed; the VII-C obstruction is unchanged (Sections “Adjoint symmetry”, “Reference profile, dilation, and cocycle”, and “Scope audit”). | (eq:parentscale); Section sec:continuity | |
| IX-A | The actual-functional carrier is defined by the metric-derivative admission test; records coefficients and boundary jets (def:Padm, def:topology). | Section sec:carrier |
For nonzero real , unchanged regular approximants do not converge to in (thm:IX1, cor:compatibility). | Section sec:continuity | |
Selected two-factor outputs belong to , but no subsequent triple is assigned (prop:knownoutputs, item 3; Section “Preservation is recorded, not extended by fiat”). | Proposition prop:partial | |
| A future compact polynomial output must pass the admission test for all configurations and directional descendants (Section “Output reservation and the admission criterion”). | (eq:admission); Proposition prop:missing |
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