Instances and question are those of the archive's Independent Set ($Lax762056.GraphProblems$), whose NP-hardness is proved there. An instance is written as the bit string $1^n\,0\,A\,1^k\,0$: the order $n$ in unary, the $n^2$ entries of the adjacency matrix $A$ in row order, and $k$ in unary.

Words. The word of an instance is this bit string with each bit written as the number $0$ or $1$, and the instances are exactly the words of this form. The parameter of a word is the length of the run of ones that ends just before its last entry; on the word of an instance it is $k$, since the last matrix entry is a diagonal entry and hence $0$.

Relation to $WH_C1_GraphProblems.IndependentSet$. That problem asks the same question for an exact solution size, on compressed sparse row words. The two problems differ only in the encoding.