Manuscript En05-C@1 · En05-C.tex · section · aa213ea6
The completed stages
Introduction and precise scope › The completed stages · lines 189–239
The supplied plan contains both theorem targets and construction targets. We address each, with its domain stated before its proof.
{}1.12
| Stage | Target | Result and boundary |
|---|---|---|
| A | Tensor-free comparison | Proved for unital -subalgebras and all global states. |
| B | Centers and preparation classes | Full center-sensitive snapshots; exact preparation-relative criterion and counterexamples. |
| C | References | Independent matrix amplification; shared-charge references require a declared joint constrained algebra. |
| D | Finite gauge demonstrator | Explicit model, regional algebras, instruments, and four operational tests. |
| E | One-layer gauge locality | Proved for specified internal Kraus devices in a locally commuting net. Not for arbitrary regional UCP maps. |
| F | Ancestry and no-signalling | Proved for that device class, with matched global device actions and complete records. |
| G | Normal channels | Proved for von Neumann subalgebras and all normal states. |
| H | Observable limits | A bounded-sequence construction and an exact finite-mode gauge subdivision limit are constructed. A relativistic field-theory scaling limit is not asserted. |
The last boundary is substantive. Completing an observable-level refinement construction for a specified model is not the construction of a continuum Yang–Mills theory, nor the discharge of every observable-limit or covariance hypothesis in En05-A or En06-A.