Natural ghost equations without an interacting quantum differential

This section distinguishes formal gauge kinematics from the released free causal derivation.

Write $q=\bar{q}+\kappa r$, with $\bar{q}$ held fixed. Define the formal kinematical rule

Equivalently, $s_{\mathrm{kin}}r={\mathcal{L}}_c\bar{q}+\kappa {\mathcal{L}}_{c}r$. Odd coefficients are placed on the left. Its leading flat rule is (eq:s0).