We present an alternative solution to nonsingular cubic moment problems, using techniques that are expected to be useful for higher-degree truncated moment problems. In particular, we apply the theory of recursively determinate moment matrices to deal with a case of rank-increasing moment matrix extensions.
"A new approach to the nonsingular cubic binary moment problem." Ann. Funct. Anal. 9 (4) 525 - 536, November 2018. https://doi.org/10.1215/20088752-2017-0066