The Kronecker-coefficient obstruction conjecture in geometric complexity theory

Let $g(\lambda,n^d,n^d)$ be a rectangular Kronecker coefficient, and let $\gamma_{\lambda,d,n,m}$ be the multiplicity of the irreducible representation indexed by $\lambda$ in the coordinate ring of the padded-permanent orbit closure. GCT obstruction conjecture. There exist $\lambda$ such that

$$g(\lambda,n^d,n^d)=0$$

and

$$\gamma_{\lambda,d,n,m}>0$$

for some $n>\operatorname{poly}(m)$.

The proposed obstruction would exploit vanishing rectangular Kronecker coefficients to separate the padded permanent from the determinant. The source gives no resolution.