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Ebenfelt's SOS conjecture for ranks of prolonged sums of squares
SOS Conjecture. If $A(z,\bar{z})\|z\|^2\in {\rm{SOS}}_n$ , then either
Conjectureopencomplex-polynomials rank-gaps sums-of-squaresarXiv posted 2 days ago

Ebenfelt's SOS conjecture for ranks of prolonged sums of squares