Proof of the Asymptotic Linearity Theorem Extension Conjecture (ALTEC)

Abstract

The Asymptotic Linearity Theorem, which proves the Fukui conjecture in a broader context, plays a significant role in the repeat space theory, which is the central unifying theory in the first and the second generation Fukui Project. Proving the Asymptotic Linearity Theorem Extension Conjecture (ALTEC) is a fundamental problem in the repeat space theory. In the present paper, we give a proof of the ALTEC using inwardly repeating fractal structures of some functions used in Matrix Art from the Niagara Project, which is part of the second generation Fukui Project. In recent years, the Niagara Project has been extended to the broader project of Science-Art Multi-angle Network, and the second generation Fukui Project is also called the New Frontier Project.