The K-theoretic matroid invariant conjecture

Let $M$, $M_1$, and $M_2$ be matroids, with $M^\perp$ denoting the dual matroid, $M_1\oplus M_2$ their direct sum, and $M_1+_2M_2$ their parallel connection. Let $g_M(t)\in\mathbb{Z}[t]$ be the matroid invariant defined in the paper.

K-theoretic matroid invariant conjecture. For any matroids $M$, $M_1$, and $M_2$,

$$g_M=g_{M^\perp},\qquad g_{M_1\oplus M_2}=g_{M_1}g_{M_2},\qquad g_{M_1+_2M_2}=t g_{M_1}g_{M_2},$$

and all coefficients of $g_M$ are nonnegative.

The conjecture is proposed to extend the results from realizable matroids to matroids realizable only in positive characteristic or not realizable at all. No resolution evidence is supplied, so it remains open.