Theorem: X-B-ii release

For the frozen scalar-only field content of X-B:

1. every constructed object is a field-degree-one element of ${\mathfrak{A}}_0$ with polynomial classical background dependence and no $\hslash$ (Proposition prop:scope);

2. the one-contraction check is an identity for the pair (A1)–(A2), symmetric and causally factorizing on that pair, and the tools of the sheet define no second pair: the pointwise square of ${\Delta }_{\mathrm{F}}$ fails the wavefront product criterion at every diagonal point (Theorem thm:nonextension);

3. the single map $R_1(V_{1,g}[h];\cdot )$ is the unique map ${\mathcal{L}}_{\mathrm{off}}\to {{\mathfrak{A}}_0}^{(1)}$ with the classical normalization (eq:sheet); every sheet-compatible contact modification is zero in ${\mathfrak{A}}_0$, and the first-order identity of X-B is independent of any such modification (Theorem thm:unique, Corollaries cor:contact, cor:ward);

4. the Branch B data are listed and not supplied (Section sec:branchB).

No time-ordered family, graviton datum, second-order quantum map, loop, state, or sharp limit is constructed, and none is excluded.

Proof. Each item cites the result that proves it.