The SOS conjecture for symmetric B₀-biquadratic tensors

Let $\mathcal{A}$ be a symmetric $\mathrm{B}_{0}$-biquadratic tensor, meaning a symmetric biquadratic tensor satisfying the $\mathrm{B}_{0}$ conditions specified in the source. An SOS tensor is one whose associated biquadratic form is a finite sum of squares of bilinear forms. SOS conjecture for symmetric $\mathrm{B}_{0}$-biquadratic tensors. Every symmetric $\mathrm{B}_{0}$-biquadratic tensor is an SOS tensor. The source states that every $\mathrm{B}_{0}$-biquadratic tensor is PSD, while the SOS property is posed as an unresolved question.