Canonical Closure of Classical Geometric Constructivism over ℝ²

This work presents the first complete and irreducible enumeration of compass-and-straightedge geometric constructions over the Euclidean plane ℝ². A total of 500 distinct constructions are rigorously defined, categorized, and formally derived under strict classical constraints. Of these, 413 are historically documented constructions, 79 are novel but provably constructible, and 8 are formally impossible but included to define the theoretical boundary of classical constructivism. Each construction terminates in a finite number of steps and adheres strictly to Euclidean geometric logic without coordinates, approximations, or analytic methods. The result defines the canonical closure of geometric constructibility in classical mathematics.