Pythagorean Unified System V9.8 Cutting-Recovery and 4D Cosmic Paradigm

This paper systematically expounds the core cognitive paradigm of the Pythagorean Unified System — Cutting-Recovery-Iterative Validation, serving as the methodological outline and reading guide for the entire series. Instead of constructing theory fragmentally, the system approaches the cosmic primitive structure through holistic cutting, model recovery and multi-dimensional verification. The cognitive path starts from intuitive 4D geometry, double cone and square double cone, and gradually derives four core elements: Primitive 1, Background 1⁰, Coupling 0, and β₁ Set (Prime Singularity Grid), and finally achieves global closure of mathematics, physics and philosophy. This paper clarifies that geometric level is insufficient for fundamental unification, and primitive mathematics is necessary to remedy structural defects of traditional theories, helping readers grasp the evolutionary logic from intuition to rigor and from form to origin.