Non-inputs and unopened constructions

The convolution coefficient and X-Enter are not inputs. X-Enter's Option A concerns readout of the convolution coefficient alone. Its Option B reference is not supplied by the ramp observable, and the ramp edge integral is not the convolution quantity $c_{\epsilon }$. Reading ${\hat{A}}_2$ would preserve an upstream identity, not prove it.

VII-A, VI, VII-C, IX-E-2, and IX-E-3 remain comparison. No cone, token, sharp insertion, or earlier kernel is identified with the ramp coordinate kernel. VII-C's hypotheses (E1)–(E4) are not assumed.

Branch B, with a quantum metric, is a different construction. There is no gravitational action, gauge-fixed graviton propagator, or metric contraction in the present sheet. A graviton tree or mixed triangle would require its own definition and analysis. Neither existence nor obstruction of those graphs follows from the scalar-only maps below.

No time-ordered hierarchy is used to fill the missing coefficient. The restricted maps are defined directly and then checked against their dynamics, support, and equation-ideal variation. This limited construction is sufficient for the stated target; it is not a substitute for a product programme on nonlinear insertions.