Two Conjectures, One Axiom

Collatz and Goldbach—one dynamic, one static; one iterates downward, one splits upward. On the surface, they seem unrelated, yet under the framework of the ECS Axiom, they share the same underlying logic:

Symmetry + Conservation → MIE Extremum → Unique Stable Structure (or Unique Extremal State) → Conjectures proven.

This is no coincidence. It is further evidence of the deep unity of mathematical structures.

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These two proofs were written in the spring of 2026. I was sitting on a bus in Luoyang, watching the street scenes flow past the window, when a thought suddenly struck me—the essence of the Collatz conjecture is “the extremum of information efficiency.” Afraid of forgetting it, I jotted down the key words on my phone. A few days later, the symmetric framework for Goldbach grew on its own.

I have not published them in mathematical journals—at least not yet. Not because they are wrong, but because the “mainstream” is not yet ready to accept the MIE Axiom. Paradigm shifts are never a matter of persuasion; they are a matter of waiting for the old generation to retire and the new generation to grow.

So I have written them into this book. This book will not be returned by reviewers, nor will editorial boards question “why the axiom holds.” It will sit quietly, waiting for the right reader to open it.

Zhang Suhang

Luoyang

May 2026