WDVV linear-reduction conjecture

Let $N$ be the dimension of the WDVV system, let $S_L$ denote its linear subsystem, and let $S_{\lambda amu b}$ denote the remaining equations indexed by $2<\lambda<\mu\leq N$ and $2<a<b\leq N$. Linear-reduction conjecture. For all $2<\lambda<\mu\leq N$ and $2<a<b\leq N$, one has

$$S_{\lambda a\mu b}\equiv 0$$

on account of $S_L$; consequently, the WDVV system can always be written in passive orthonomic form. This is the explicit formulation of the preceding reduction expectation, and its general validity is not proved in the supplied text.