Title: Non-Euclidean Vector Space Geometry - Computational Reconstruction

Jincheng Zhang

Published Sep 4, 2026• 0 citations

Abstract

This paper investigates the potential of constructing geometric representations of vector spaces beyond Euclidean space, aiming to facilitate novel geometric analysis through the introduction of a 'Quantum Geometric Lattice.' The core mechanism centers around the creation of a dynamically shaped system of interconnected quantum states – the 'Quantum Geometric Lattice' – that subtly modifies the vector space's geometry. We explore the potential for revealing hidden geometric relationships and utilizing this framework for advanced computational reconstruction and data analysis. The research builds upon established concepts in quantum mechanics and geometric analysis, proposing a novel approach to represent and manipulate vector spaces in a fundamentally different way. The paper details the design and implementation of the Quantum Geometric Lattice, its operational principles, and preliminary results demonstrating its impact on geometric reconstruction and data visualization. The ultimate goal is to establish a computational method for generating geometrically rich representations, pushing the boundaries of traditional geometric analysis.

DOI: 10.5281/zenodo.22289309

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