The fractional linear generation conjecture for higher Chow groups

Let $K$ be a field satisfying the rank conjecture of Suslin, and let $CH^p(K,p+q)$ denote its cubical higher Chow groups, where $q\geq 0$. A fractional linear generation conjecture asserts that these groups are generated by fractional linear cycles. This would mean that Grassmannian homology already computes the higher Chow groups of number fields, linking the Grassmannian complex with explicit representatives in higher Chow theory.