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Mathematical Framework for Formalizing Pencil-Puzzle Rules

A formalism for defining and systematizing the rules of grid logic puzzles (Slitherlink, Sudoku and other Nikoli puzzles). It defines grid elements (points, edges, cells) and their positional relationships such as adjacency, iteratively composes them into structures underlying a rule, and attaches constraints and solution domains that guarantee solvability and coherence, giving a unified basis for computationally generating entirely new puzzle rules rather than new instances of known ones.