Pythagorean Unified System V9.9 A Unified Conclusion on Geometry ⇌

The fundamental dilemma in traditional mathematics and physics is the long‑standing separation among algebra, geometry, and physics. Algebra depends on symbols, geometry on intuition, and physics on phenomena, while none possesses a common origin and unified framework. Based on the Pythagorean view that “all things are numbers”, this paper establishes a globally unified system that is self‑closed, self‑driven, and self‑conserving, with the primitive state 1 as the sole starting point and β₁ as the unified endogenous dynamic. This article is a concise final version with complete and rigorous core logic. Readers seeking detailed derivations, structural proofs, and dynamic frameworks may refer to the archived full versions via the DOI links provided. This work rigorously proves the natural equivalence and isomorphism between geometry and algebra, as well as the unity of mathematical logic and physical reality. It fundamentally resolves the underlying defects of traditional systems and lays the foundation for a new mathematics and new physics.