Manuscript XVI-D@1 · XVI-D.tex · section · b73c6f4a
Provenance and dependency structure
Provenance and dependency structure · lines 233–291
The available material comprises the supplied XVI-A, revised XVI-B, original XVI-D, XVI-E, and XVI-F-v3 texts, together with predecessor statements reproduced in those texts and the supplied coverage material.
Complete XI-B, XII-D, and XVI-C sources are not supplied here. References to their internal labels identify reported passages; they do not certify a full-file or full-series audit.
Four kinds of statement are distinguished:
Imported formula or definition: retained with its stated convention and domain.
Imported theorem: used only within the explicitly recorded quantifier.
Proof in this manuscript: a calculation or argument given below.
Compatibility obligation: an identification not supplied by the preceding proof.
The main dependency structure is noncircular:
| Input or result | Provenance | Use here |
|---|---|---|
| Prepared witness source | XVI-B, source-level formula | Input to the response calculation |
| Diagonal response existence | Reported XII-D response theorem | Defines real polarization |
| No-decay uniqueness | Proved in Section sec:uniqueness | Bilinearity and witness identification |
| Compact scalar Green theorem | Reported XI-B, lem:Green | Scalar completion on compact forcing |
| Coordinate candidate | Formula also present in XVI-E/F-v3 | Reproved directly here |
| Root and later compatibility | XVI-E and XVI-F-v3 | Separate later-results record |
Only the source calculation of XVI-B is used as a premise. Its later-results summary of XVI-D is not used to prove XVI-D.
General wave-equation background is available in BGP; the no-decay uniqueness argument needed here is given explicitly below rather than left as an external premise.