Smooth multipliers do not supply missing products

For a fixed smooth multiplier $a$ and a distribution $u$,

This standard microlocal fact Hormander, also recorded as a conditional tool in XVI-A XVIA, is not a subtraction prescription. It supplies no uniform estimate for an arbitrary scale-dependent multiplier family, no extension of an undefined product, and no loop regulator.

The ramp disappears from the coordinate density in a specified Cauchy limit. It was never a regulator for the characteristic quantum graph or for a Feynman-kernel square.