Manuscript XIII-A@1 · XIII-A.tex · section · f56e91c7
Three readings and the named restriction problem
Three readings and the named restriction problem · lines 272–316
The endings Constructed, Proved obstructed, and Unresolved refer to a specified object and its stated requirements. They are not ordered assertions about every possible successor theory. In particular, a classical cancellation can be constructed while its naive quantum implementation is obstructed.
| Reading | Object | Ending here |
|---|---|---|
| Evaluation-only | Evaluate prescribed classical lifts on ; retain the existing carrier without a new quotient. | Constructed under the support hypothesis. |
| Reduced algebra | Select compatible observables and prove a separate reduction theorem. | Unresolved. |
| Completion | Add a declared term or co-transformation cancelling the auxiliary remainder on the full shell. | Unresolved. |
The principal question is whether the first reading can be implemented by simply quotienting the entire inherited carrier by coefficientwise vanishing on . We give a negative answer to that particular question. We do not select the observable subalgebra, equivalence relation, or product of a different reduction.
The obstruction uses regular linear fields. It does not require a singular composite product, an extension at coincident points, or a renormalization condition. Its mechanism is the existing central commutator. The ordering calculation concerns functionals, not movement of configurations by a change of product data.