The FSEANI conjecture for the real and complex fields

Let $n\in\mathbb{N}$. A field $\mathbb{K}$ is an $n$-FSEANI if the parametric family of systems of equations given by (EE) has a non-zero solution in $\mathbb{K}$ for every choice of parameters $a_{ij}$ in $\mathbb{K}$ making (EE) a non-trivial zero-intersect-evolution-axis system. FSEANI conjecture. The fields $\mathbb{R}$ and $\mathbb{C}$ are $n$-FSEANIs for every $n\in\mathbb{N}$. This would identify the real and complex fields as universal fields for the existence of non-zero idempotents in the relevant simple evolution algebras. The preceding examples show that $\mathbb{Z}_{3}$ and $\mathbb{Q}$ are not $2$-FSEANIs, while the assertion for $\mathbb{R}$ and $\mathbb{C}$ remains open in the supplied source.