The exact affine gauge propagator

This is a general algebraic proof in the declared trace-four algebra, not an interpolation from finite momenta. The DRED contraction prescription and overall Feynman factor remain scientific inputs. On $k^2=0$, a prescribed boundary value is required; this is not pointwise inversion there. At $\xi =0$, the eliminated kinetic expression is undefined. The predecessor's action-Hessian check is attributed to 1_kincheck.py, not newly executed.