Phistomefel’s Theorem (and the more general "set equivalence theory" described in the article) pops out directly from a standard technique known as the "Linear Programming relaxation" for Sudoku.<p>Essentially, the Linear Programming relaxation of a puzzle is a standard way of approximating the solution space with a system of linear equations and inequalities, replacing discrete yes/no answers to questions like "is the digit inside this box a 7?" with real numbers between 0 and 1 (which can be interpreted as probabilities, if you like). This system of linear inequalities and equations can then be solved efficiently with techniques from convex optimization.<p>Even the example from the Cracking the Cryptic video, with the conclusion that those three boxes at the bottom have to be 1, 2, and 3 in some order, would be deduced immediately from the Linear Programming relaxation of Sudoku. You don't need ontological remodeling when you know how to apply convex optimization :)