Depth-one reduction conjecture for the derivative sums in the $f_6$ family

Let the $f_6$ family denote the family of derivative sums discussed in the paper, and let the MZV algebra be the algebra of multiple zeta values. The single zeta values are the values $\zeta(m)$.

Depth-one reduction conjecture. Every derivative sum in the $f_6$ family belongs to the subalgebra of the MZV algebra generated by the single zeta values $\zeta(m)$; no irreducible multiple zeta value of depth at least two occurs.

The paper proves depth-one reductions through weight eleven, but does not settle the full derivative tower. Thus the all-orders assertion remains open.