Title: Non-commutative Geometry for Computational Complexity Theory

Jincheng Zhang

Published Sep 7, 2026• 0 citations

Abstract

This paper explores the potential of non-commutative geometry as a foundational concept for analyzing computational complexity. We propose a novel framework where the order of operations fundamentally shapes the landscape of computational complexity, suggesting that inherent non-commutativity is a key limiting factor. The core mechanism involves introducing a geometric representation where the notion of order is paramount, leading to unexpected and potentially exploitable limitations on algorithm design. This work aims to provide a new perspective on complexity theory, moving beyond traditional algebraic approaches and embracing the geometric implications of computation. The paper details the proposed geometric framework, outlines the identification of critical points through geometric anomalies, and discusses the implications for understanding the fundamental constraints on computational performance.

DOI: 10.5281/zenodo.22614491

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