A complete conditional affine application

Pure-trace probes in particular cannot authenticate an unrestricted metric-slot kernel. A smooth trace-free tensor $a^{\mu \nu }$ produces the nonzero compact kernel $a^{\mu \nu }(x)a^{\rho \sigma }(y)$, invisible to every pair of pure-trace inputs. This is the blind-sector control recorded in Cheung's XVIII-A CheungXVIIIA.