Ok. Distribution of scalar mutliplication with respect to field addition doesn't hold.
we should have
\((a+b)\vec{v} = a \vec{v} \oplus b \vec{v}\)
let's take a look
\((a+b)\vec{v} =\{(a+b)v_x,(a+b)v_y\}\\ a\vec{v} \oplus b \vec{v} =\left \{\sqrt[3]{a^3 v_x^3+b^3 v_x^3}, \sqrt[3]{a^3 v_y^3+b^3 v_y^3 }\right \}=\\ \left\{\sqrt[3]{a^3+b^3}v_x,~\sqrt[3]{a^3+b^3}v_y \right\}\\ \sqrt[3]{a^3+b^3} \neq a+b\)
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