Manuscript Em01-B@3 · Em01-B-v3.tex · section · 69189992
The mathematical object
Main results, dependencies, and conventions › The mathematical object · lines 275–331
The immediate object is a local family
obtained by smoothing the grouped crossed distribution and keeping the internal kernel exact. Its value on the named kernel is the complete retained contraction, not the full globally assembled quantum coefficient.
The new conclusions are summarized below.
| Result | Exact dependency |
|---|---|
| Complete regularized map and descent | Defined internal distributions, the explicit vertex, and smooth crossed coefficients. |
| Internal-frequency estimates | The fixed retarded cone kernel and its Fourier transform; no crossed-line product. |
| Ordinary-product convergence | Localized angular separation and normal-topology operation theorems. |
| Complete-contraction growth bound | Order-zero internal seeds, at most four internal derivatives, and finite order of the compact crossed distribution. |
| Characteristic-limit criteria | Additional weak convergence or summable Cauchy estimates; for a map theorem, uniform input and Fourier estimates. |
| Characteristic projection and ambiguity | The explicit characteristic submanifold and compact distributional pushforward. |
The complete supplied XIV-H/I/J sources fix the retained instance XIVH,XIVI,XIVJ. Their internal formulas are reproduced below. Their identification with the designated observable Hessian, global contact inventory, and global canonical-domain construction remain inherited inputs. The new distributional theorems are valid for every fixed smooth source-coefficient array satisfying the stated finite differential form.
The internal-module conclusions are checked within XIV-I's named finite module. No equivalence with a general intersecting-Lagrangian calculus is asserted. Source-history details are placed in Appendix app:evidence.
Displayed formulas in this passage
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