What question did this study set out to answer?

This work aims to investigate the implications of the Hua-He core formula across multiple mathematical domains.

June 14, 2026Open Access

Hua‑He Core Theory: Two Deep Paths from the Core Formula 2 i 3 r G - 2 j 3 t Q=2 Differential Equations and Analytic Number Theory

Key Points

This work aims to investigate the implications of the Hua-He core formula across multiple mathematical domains.
Explores a differential approach leading to integrable flat geometry.
Interprets the core formula as a Diophantine equation using Baker's theorem.
Examines the governing identity's impact on discrete dynamics and the scarcity of solutions.
Establishes a synchronous evolution for exponents in the core formula.
Demonstrates connections between continuous conserved quantities and discrete dynamics.
Illustrates the core formula's role in governing solutions to exponential Diophantine equations.

Abstract

The core formula 2i3rG−2j3tQ=2 is the unique axiom of Hua‑He Core Theory. This paper explores two independent deep directions: (1) a continuous/differential approach, which reveals that the exponents must evolve synchronously and leads to an integrable flat geometry; (2) an analytic‑number‑theoretic approach, where the formula is interpreted as a Diophantine equation and studied via lower bounds for linear forms in logarithms (Baker’s theorem). The two paths together show that the same elementary identity simultaneously governs discrete dynamics (Collatz type), continuous conserved quantities, and the scarcity of solutions to exponential Diophantine equations (Fermat, Catalan, Beal). A unified summary table illustrates the multiple levels at which the core formula operates.

Hua‑He Core Theory: Two Deep Paths from the Core Formula 2 i 3 r G - 2 j 3 t Q=2 Differential Equations and Analytic Number Theory

Key Points

Abstract

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