Unknown coefficient in the motivic Segre Thom polynomial for \overline{A2}

Determine the coefficient of the Grothendieck polynomial g_{22} in the motivic Segre Thom polynomial mSTp(\overline{A_2},ℓ=0) given in the displayed expansion (equation (13)), and extend the computation to the remaining unknown coefficients of this series.

Background

Motivic Segre (MS) classes are the K-theoretic, \hbar-deformed analogues of fundamental classes that retain functoriality properties with both push-forward and pull-back.

For the closure of A_2, the paper presents a partial MS Thom polynomial expansion in Grothendieck polynomials; the first missing term explicitly identified is the g_{22} coefficient, marking a concrete computational gap.