The Base-5 Nuclear Source Theory is a complete mathematical system rigidly constructed from the odd-number expression N=2i5rR−1=2j5pQ+1, governed by ten constraints. It uniquely maps every natural number to a set of nuclear coordinates (i,j,r,p,R,Q), covering odd numbers, even numbers, zero, and the full range of positive and negative integers. The system spontaneously generates generating functions, q-difference equations, nuclear continued fractions, L-functions and zero structures, legitimate dynamics and conservation operators, and extends to arithmetic topology and TQFT. Ultimately, via the golden ratio ϕ and a modulo‑6 core square continued fraction, the theory rigidly locks the fine-structure constant 137.035999084236472859310254789137.035999084236472859310254789 and the electron charge constant, revealing that the fine-structure constant is the "expression" while the golden structure constant is the "inner construction." Base 3 and Base 5 share the same skeleton, together forming the first binary system of the Nuclear Source Theory, achieving a unification of number theory, integrable systems, quantum physics, and arithmetic topology.
Kang A. (Tue,) studied this question.
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