Convolution premises: the inputs of Options A–D

Fix the regulator, switch, Cauchy prescription, observation test, and supported gauge algebra of X-A–Convolution. Its copied identities and positive witness are

Here the operators and tests retain their meanings in the convolution source; their kernels are not needed below. The action Noether identity is already zero on ${{\mathfrak{g}}_{\mathfrak{U}}}^{\mathrm{C}}$. The inherited first-order relational gap is $X_{\xi -S_{\epsilon }\xi }$, and no term at order ${\kappa }^2$ repairs that first coefficient Convolution.

Let $a$ be its first evaluated smeared coefficient. The inherited witness orbit is

Every real multiple $\lambda {\xi }_{\ast }$ remains in ${{\mathfrak{g}}_{\mathfrak{U}}}^{\mathrm{C}}$. Consequently this coefficient orbit covers $\mathbb{R}$. It is an orbit of the first-order coefficient, not a claim that a coupling expansion is uniform in arbitrarily large $\lambda$.