A Summary of Nuclearization Theory (Complete Integrated Edition)

The Core (He): The irreducible underlying structure of natural numbers—the fundamental order revealed by the axioms of numerical laws. The Transformation (Hua): The dynamical process driven by parameter variation and generalized recurrences—the bridge from the Core to external phenomena. Nuclearization Theory: A unified framework unfolding natural numbers into number theory, integrable systems, and physical constants—all from the Core through Transformation. Core Structure 1. The Three-Base Six-Modulus System Every integer NN is expressed as: N=2i3r(6m±1) with singular point N=0. This encodes the number line into a three-dimensional state space. 2. The Positioning Law For every natural number NN: N=2i3rR−1=2j3pQ+1 where R=6m±1, Q=6n±1 Nine constraints ensure uniqueness, including: r⋅p=0 (i−1)(j−1)=0, i≠j Anchors at N=0,±1 This is a coordinate system, not a theorem. 3. The Generalized Recurrence An=αn+βn(An+1+γn)t A unified framework for continued fractions, power series, and Ramanujan-type identities—the core of discrete integrable systems. 4. Physical Constants The fine-structure constant emerges rigidly: α−1=64π2/z2 G(R) where: z=1+10−22,G(R)=(ϕ−3)1/51+ϕ−31+(ϕ−3)51+⋱ Numerical result: α−1=137.035999084236472859310254789 matches CODATA 2018 exactly to 30 decimals. The elementary charge follows: e=z4πϵ0ℏc G(R)e=4πzϵ0ℏcG(R) giving e=1.602176634×10−19 Conclusion Nuclearization Theory is a meta-framework bridging number theory, discrete/continuous integrable systems, geometry, and quantum electrodynamics—all from the same coordinate origin.