Degree visibility of rectangular catalecticants #
Every entry queried by the degree-d, split-k catalecticant has total degree
exactly d. Thus all splits factor through the same degree-d homogeneous
component; only the subsequent flattening changes with k.
Every queried exponent has Finsupp degree exactly degree.
Coefficients queried by the rectangular catalecticant vanish below total
degree degree.
Lower-total-degree polynomials have zero rectangular catalecticant.
Lower-total-degree polynomials are feature-invisible.
The rectangular catalecticant only sees the degree-degree homogeneous
component.
Every split factors through the common critical homogeneous layer.
A zero critical component is invisible at every split.
A rectangular Waring linear form is homogeneous of degree one.
A charged rectangular Waring term is homogeneous of total degree
degree.
Projecting a rectangular Waring term to its critical layer leaves it unchanged.