Manuscript XI-B@1 · XI-B.tex · section · 063b989e

The VII-C non-import checklist

The VII-C non-import checklist · lines 1198–1259

VII-C concerns a sharp zero-Cauchy insertion, a fixed Hadamard Wick matrix in the opposite signature, and a specified normal-topology extension. Those are not the data of the causal polynomial algebra constructed here VIIC.

For precision, its four extension requirements are recorded below. “Unmet” means not established or not instantiated by this manuscript, not disproved for every possible successor construction.

	VII-C requirement	Status in XI-B
E1	The old microcausal Wick algebra embeds into a Hausdorff locally convex $C [[ℏ]]$ -algebra, with its fixed Hadamard Wick product unchanged.	Unmet. We construct a causal polynomial algebra, not that Hadamard Wick embedding.
E2	Sharp insertions $Q_{Σ} (B_{f})$ are admitted, with $[Q_{Σ} (B_{f})]_{ℏ^{0}} = B_{f}$ on all smooth configurations.	Unmet. No sharp insertion or quantum relational composite is admitted.
E3	Admission on the stated degree- $(1, 1)$ kernel stages is sequentially continuous in the normal topology and agrees with the old regular inclusion; the regularized insertions converge to the sharp element.	Unmet. No such admission map or topology is constructed.
E4	Multiplication is hypocontinuous on bounded sets, and the field-independent $ℏ^{3}$ coefficient map is continuous and agrees with old coefficient extraction.	Unmet as a topological package. Our product is algebraic; no specified locally convex continuity result is proved.

Formal coefficient extraction is available algebraically. That does not establish E4. Likewise the tensor $P$ derived from the XI-A operator is not an imported Hadamard block. A causal inverse does not select a positive-frequency bisolution.

We do not form the word $B_{f} ⋆ W_{g} ⋆ B_{f^{'}}$ , do not evaluate a reflected light-ray residue, and do not subtract one. There is no conclusion here that the ramp resolves VII-C's obstruction, nor that VII-C obstructs the present restricted free algebra.