Possibility-Space Geometry: A Minimal Synthetic Foundation for Classical Mathematics

This paper establishes a minimal synthetic foundation for classical mathematics, deriving Euclid's Elements, the real number system through Conway's surreals, the complex plane, and probability measures from one axiom (a point exists), one definition (a geometric object is the possibility-space of a specification), and one constraint (self-consistency). The central structural result is that two points carrying a configuration force a third point by inference alone, with the resulting triangle being the unique fixed point of polygonal diagonalization. Classical mathematics is shown to be the characterization of a single structural object: a point with attached infinite coherent possibility-space.