Pythagorean Unified System V9.22: Primitive Unification Theory of Pure Mathematics Core Branches

Based on the pure mathematical axiomatic framework of the Pythagorean Unified System (Version 9.2), under the conditions of global closure, primitive conservation, and coupling closed-loop, this paper systematically reconstructs five core branches in pure mathematics: 1. The primitive resolution of set theory and Russell’s paradox; 2. The unified interpretation of real number theory and the continuum hypothesis; 3. The primitive unification of group theory and the interpretation of symmetry conservation; 4. The primitive generation mechanism of topological structures and dimensions; 5. The breakthrough of Gödel’s incompleteness theorems and the proof of system completeness. This paper shows that the paradoxes, undecidable propositions, formal deficiencies, and ontological gaps in traditional mathematics can all be uniformly solved in a globally closed primitive system without contradiction, constructibility, and provability. All mathematical structures can be uniquely generated from the Primitive Element 1, Background Element 1⁰, Coupling Element 0, and primitive operations, realizing the ultimate closure and unification of the mathematical foundation.