By Vitaly Bergelson, Neil Hindman and Kendall Williams. Author-hosted primary manuscript: people.math.osu.edu/bergelson.1/BHW_PolynomialMT.pdf
Definition1.5 and Theorem1.6 specify the positive-coefficient separated-block systems and their monochromatic sum subsystems; Theorem1.4 states the underlying Milliken-Taylor theorem.
By Neil Hindman, Imre Leader and Dona Strauss. Proceedings of the Edinburgh Mathematical Society46,45–61. DOI: doi.org/10.1017/S001309150200010X
Author-hosted final manuscript: nhindman.us/research/separate.pdf
Definition1.5 and Theorem1.7 give compression and the positive-rational-proportionality criterion for simultaneously monochromatic positive-coefficient systems.