Li Jianming Conjecture (Yuanzhou, Yichun, Jiangxi) — Unified Coupling Conjecture of Four Fundamental Mathematical Constants

Abstract

The imaginary unit i, Euler's number e, π and golden‑ratio φ are four fundamental constants in modern mathematics and theoretical physics, corresponding to complex number system, continuous evolution, rotational topology and self‑organizing optimal proportion respectively. Traditionally, only scattered low‑order relations among them are known, lacking a unified, hierarchical and self‑consistent high‑order coupling framework. In this paper, based on homogeneous linear constraints, complex transcendental zero‑point theory and analytic structure of complex‑parameter infinite‑product, we propose the Li Jianming Conjecture. It constructs a three‑level nested closed‑loop coupling system consisting of finite algebraic constraints, local transcendental dynamics on complex‑plane and infinite‑dimensional global analytic field, putting forward a set of cross‑domain open propositions connecting number theory, complex analysis and theoretical physics. Further research on this conjecture may provide new perspectives for exploring deep inner connections among basic mathematical constants.