| k | - The *signed* degree k of the k. If k >= 0, this means that the degrees of freedom are k-forms, and are stored
in lexicographic order according to the basis of k-forms constructed from the wedge product of 1-forms. So for example,
the 1-form basis in 3-D is (dx, dy, dz), and the 2-form basis in 3-D is (dx wedge dy, dx wedge dz, dy wedge dz).
If k < 0, this means that the degrees transform as k-forms, but are stored as (N-k) forms according to the
Hodge star map. So for example if k = -2 and N = 3, this means that the degrees of freedom transform as 2-forms
but are stored as 1-forms.
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