NP-hardness conjecture for recognizing f-vectors of fixed-dimensional polytopes

Let $d\ge 4$ be fixed. An $f$-vector is a vector recording the face numbers of a $d$-polytope, here written as

$$f=(1,f_0,\ldots,f_{d-1}).$$

NP-hardness conjecture. It is NP-hard to decide if a given $N$-bit vector $f=(1,f_0,\ldots,f_{d-1})$ of positive integers is the $f$-vector of a $d$-polytope.

This conjecture is proposed as an explanation for why the $f$-vectors of $d$-polytopes are poorly understood when $d\ge 4$. Its status is not specified in the source.