Title: Hyperdimensional Geometry and Topological Data Analysis

Jincheng Zhang

Published Aug 31, 2026• 0 citations

Abstract

Hyperdimensional geometry, a rapidly evolving field, presents a compelling challenge to traditional geometric analysis. This paper explores the application of advanced quantum entanglement principles to identify and quantify topological order within hyperdimensional spaces. We propose a novel framework, termed 'Quantum Fingerprint Resonance' (QFR), which utilizes entanglement to create a 'quantum fingerprint' that directly reveals underlying topological structures. This framework has the potential to revolutionize our understanding of complex systems, offering a new approach to identifying patterns and ordering within data previously inaccessible to conventional methods. The core claim centers on the development of a robust and automated methodology for extracting topological information from hyperdimensional data, driven by the inherent properties of quantum entanglement. This research directly addresses the limitations of current topological analysis techniques by introducing a fundamentally new perspective, promising significant advancements in data interpretation and potentially unlocking new scientific discoveries.

DOI: 10.5281/zenodo.22197644

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