Manuscript VII-H@1 · VII-H.tex · section · d20d2a9f
The complete first-order contraction and its domain
The complete first-order contraction and its domain · lines 747–777
| Operation | Domain and justification |
|---|---|
| Oriented wavefront product; no opposite covectors | |
| Retarded restriction | Defined away from the origin; no multiplication at the tip is assumed |
| Tip extension | Constructed explicitly in Section sec:extension |
| Joint pullback | The difference map is a submersion |
| Compact observation | Proper integration in (eq:joint-relative) |
| Differentiation | Weak distributional differentiation, not a sharp boundary limit |
The wavefront assertions use the product and pullback calculus Hormander. Normal-topology continuity theorems apply only on compatible cones and support-proper stages BDH; no unverified characteristic product is introduced.