AbstractRecent theoretical progress and major advances in computational methodology for spinodal and critical points make Pulse‐Induced Critical Scattering (PICS) a fast and reliable tool for examining statistical mechanical hypotheses, as expressed in the free energy of mixing function for solutions of linear polymers, and for measurement of the moments Mr = Σiwimir of the molecular weight distribution. Theoretical interpretation of measured phase diagrams has been hampered by 1) a lack of sufficiently reliable information on Mr(r = 1, 2, 3) of samples available from standard sources, and 2) the mental effort required in deriving spinodal and critical point equations from the increasingly complex free energy of mixing functions via the determinants of Willard Gibbs. Three strategies help to counter these difficulties: 1) Two molecular weight distributions (MWDs) are called r‐equivalent if they share at least the first r moments; computer software is available to determine the mixture of [r/2] sharp fractions which is r‐equivalent to a given MWD; thus the mixing of a small number of components gives access to an unlimited range of mixed samples whose moments are known (in terms of those of the components) to an accuracy set only by the analytical balance. 2) A spinodal truncation theorem (and critical point conjecture) exploits the concept of r‐equivalence since they determine the set of moments on which spinodal and critical point loci depend in addition to those moments featuring in the free energy expression. 3) Application of powerful algorithms of the QR‐type to the eigenvalue problems posed by the Gibbs spinodal and critical conditions have removed the necessity for prior excursions into the algebra of determinants by the human experimenter, since now spinodal and critical points can be numerically computed easily and directly from any postulated free energy function, especially when we employ the truncation theory and the notion of r‐equivalence. In consequence, the rapid feedback now possible with computer explorations of theoretical hypotheses is helpful in advancing the thermodynamics of polymer solutions and exploiting more fully the tools, such as PICS, for monitoring the relevant effects experimentally.