I'll answer my own question for posterity's sake.
After reading the article a few more times, I'm 97% sure that a "vanishing
variable" in this case is a variable with a value of zero in a given basis.
Likewise a "non-vanishing variable" would have non-zero value in a given
basis.
If anyone thinks I'm off on this assessment or knows of some other potential
definition of vanishing, please post a clarification.
Thanks.
Joey
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