Term Coding: An Entropic Framework for Extremal Combinatorics and the Guessing--Number Sandwich Theorem

Classical existence problems in extremal combinatorics ask whether finite operations can satisfy prescribed identities universally. Term Coding replaces this yes-or-no question by a graded one: for a finite system $Γ$, the maximum code size $S_n(Γ)$ is the largest number of satisfying assignments at