Both internal placements of K 5

It does not permit an unproved generalized composition with the quantum cross-lines. Such a composition is the later I3 obligation. No common product phase, resolved base space, frequency-regulator family, or characteristic prescription for a new product is introduced.

The construction below is a finite, explicit amplitude module. It is not an assertion of a general paired-distribution calculus.

The endings are applied to the object at the gate reached:

1. Constructed: that object has its stated domain, amplitude or degree, and wavefront control.

2. Proved obstructed: an incompatibility excludes every candidate in Definition def:class.

3. Unresolved: a necessary amplitude, common composition, section, prescription, or J-gate estimate is missing.

The earlier exclusion of a single ordinary Lagrangian is not a universal obstruction to this class.

Only admission of ${R_1}^{(1)}$ in ${\mathcal{E}}_H$ at I6 could open XV-B. An I2 amplitude theorem opens I3 only.

2a: the fixed retarded multiplier and its transition pole

convention

For a relative variable $r=(t,\mathbf{x})$, use

Inverse Fourier transformation has the factor $(2\pi {)}^{-4}$. Thus ${{\partial }_r}^{\beta }$ has multiplier $(i\kappa {)}^{\beta }$, where

The $\kappa$ in this section is a frequency variable, not the interaction coupling.

All Fourier calculations concern the already fixed distribution $R$. They choose no new characteristic value for (eq:target).

The tempered Fourier transform of $R$ is

On $\rho >0$,

It is homogeneous of degree $-2$ in the distributional sense.

Proof. The spatial Fourier transform of (eq:R) is

with continuous value $\Theta (t)t$ at $\rho =0$. Multiplying this existing distribution by $e^{-ϵt}$ on its support and taking its temporal Fourier transform gives

The damped distributions converge to $R$ in ${\mathcal{S}}^{\prime }({\mathbb{R}}^4)$, as follows directly from its cone formula and the rapid decay of Schwartz tests. Fourier continuity gives (eq:MR).