Example: Highest presentation degree is not intrinsic

For a nonzero distribution $R(r)$ in independent variables,

The two summands separately are nonzero and opposite. Thus a chosen polynomial-degree splitting of a presentation does not automatically descend to reconstructed kernels.

This does not rule out a quotient filtration defined from images of filtered presentation spaces. It rules out treating a representative-dependent highest term as an intrinsic joint symbol without the required descent theorem CheungXIVJ,CheungXVB.