The spectral containment conjecture for homogeneous multiaffine stable polynomials

A homogeneous multiaffine stable polynomial $p\in\mathbb{R}[x_1,\ldots,x_n]$ has the spectral containment property if, for every symmetric matrix $A\in H(P)$, some eigenvalue vector of $A$ belongs to $H(p)$. Spectral containment conjecture. Every homogeneous multiaffine stable polynomial has the spectral containment property. The paper establishes several special cases and reports computational evidence, but the general assertion remains open.