Manuscript XV-B@2 · XV-B.tex · section · 4d3f12e8
Status of the inherited problem
What is still required for the full map › Status of the inherited problem · lines 2176–2226
| Gate | Required object | Status in this revision |
|---|---|---|
| B1 | Full joint characteristic map | Exact lifting and local null tests proved. No full graph lift and admissible null cancellation constructed. |
| B2 | Joint section and controlled remainder | No section for the required complete coefficient constructed. |
| B3 | Uniform transverse estimates | No target transverse estimate transferred from internal degree or frequency estimates. |
| B4 | Contact compatibility | Support obstruction and local point correction proved in their stated classes; no complete graph compatibility established. |
| B5 | Output wavefront theorem | No new complete output theorem after the required quantum composition and pushforward. |
| B6 | Normalized coefficient and admission | No identified normalized admitted by (eq:admission). |
These are descriptive labels for this paper, not a redefinition of the predecessor gates. XIV-H's historical internal amplitude stop was addressed by the named XIV-I amplitude construction. The remaining operation is the stronger joint characteristic map, reported unresolved at I3 and J2 CheungXIVH,CheungXIVI,CheungXIVJ.
Failure of a sufficient ordinary-product hypothesis is not a universal nonexistence theorem for a larger declared class. Conversely, it does not authorize a generalized product without its construction and estimates. The present paper neither retries the failed shortcut nor supplies an alternative full composition.
No interacting differential is applied to an absent quantum coefficient, and no quantum Ward defect is formed.