Even a local cone field does not determine Einstein curvature

The distinction is between a positive constant ambiguity for one affine quadratic form and a positive function in a local metric extension. Allowing the latter introduces new data; it is not merely fixing the former's units.

The conformal calculation is independent of any field equation. It also shows why “Einstein curvature of a conformal class” is not a well-defined representative-independent source for the proposed matching.