Status ledger and corrections

{}1.12 {@{}p{0.30}p{0.65}@{}} Object or result & Current status

Object or result & Current status, continued

Classical polarized kernel & Established under the revised XVI-H root/source inputs. Its general test action is (eq:t-test).

Matching XII-D admission kernel & Exact matching under the explicitly supplied domain and normalization premises: Proposition prop:match.

Direct classical admission & Established as an imported-premise consequence: Theorem thm:admission. The old blanket non-admission disclaimer is removed.

Prepared free-shell class & Contains the admitted representative $t_{\mathrm{D}}$. On data with the frozen obstruction, it cannot be the excluded frozen class: Corollary cor:oldclass.

Trisolution cone exclusion & Consequence of the separately stated transport premise and imported $Z_3$ bound. No new classical wavefront calculation is performed.

Witness matching to $j_{\lambda }$ & Established in revised XVI-H using current XVI-E/F/G. It is partial evaluation, not the graph kernel.

Ambient tensor propagator & Explicitly chosen and identified: Proposition prop:DF. $D_F=\mathcal{P}d$, with $(-\square \mathcal{P})D_F=\mathrm{i}\mathrm{id}$. The slab restriction is justified on interior sources.

Off-diagonal edge product & Proved for the chosen propagator, including nonzero null-related pairs: Proposition prop:product.

Cubic Hessian and derivative recipe & Defined by exact jet differentiation: (eq:L)–(eq:Hessian). Total vertex derivative order is at most two.

Reduced graph sector & Defined and proved distributional on $y\ne w$: (eq:Vblock)–(eq:U), Theorem thm:reduced.

Nonvanishing & Proved for an open-index vertex block when the switch is nonzero: Proposition prop:nonzero. Not asserted for every contracted or attached sum.

Scaling degree & Vertex-only bound six; source-decorated bound eight. Local transverse upper bounds, not a sharp total degree: Proposition prop:sd.

Diagonal extension & Existence and point-building-block ambiguity established: Theorem thm:extension. Normalization constants unchosen.

Compressed root attachment & Product and proper-pushforward tests proved under $\mathrm{WF}(B)\subset Z_2$: Theorem thm:attach. No root singular support is deleted.

Smeared root-attached coefficient & A family exists for extension choices: Corollary cor:coefficient. No normalized member is selected.

Unfolded root graph & No separate product theorem for every internal $z$-factor is claimed. The compressed inherited root is the route used.