Successor problems and final separation of conclusions

The closed statements are:

and, at compact $g$,

The independently defined Newton–wave composition has the form and witness of Section sec:contrast.

The following four questions remain separate.

1. Dense-TT representability. Does there exist $J\in \mathcal{E}$ representing the raw or sectioned pairing on a specified infinite-dimensional TT space? The 2-plane current and the $\mathcal{S}$ classification do not decide this.

2. Adiabatic switch. Existence or obstruction for $g\to 1$ in the external and one-oscillator retarded coefficients. Compact-support continuity is not that limit.

3. Second vertex product. Construct $T_2(V,V)$ and its retarded subtraction. The absence of a degree-four parameter in $R_{1,1}(V,\varphi (f))$ says nothing about this product.

4. Graviton loops and a local metric field. Replace the oscillator-valued wave by a local linearized-gravity field and construct the corresponding causal products. The finite-mode commutator (eq:nonlocalcomm) already fails the required locality.

None of these questions asks to identify the Newton–wave cubic form with either retarded coefficient. Their metric arguments, quantum degrees, and construction steps are different by definition.

Figure fig:closed-and-successor separates the established conclusions from the four stated successor problems.