On the Real Line as a Highly Restricted Structure
Year: 2026
Type: article
Abstract: The real line is commonly regarded as a primitive and exhaustive structure for the representation of magnitude. This work proposes an alternative structural reading in which the real line is understood as a geometric configuration obtained through an extreme restriction of orientational degrees of freedom. By interpreting linear representation as the preservation of only two opposite directions, the article analyzes how properties such as sign, total order, and commutativity arise as consequences of this restriction rather than as primitive axioms. The analysis situates the real line as a rigid limit case within a broader hierarchy of geometric representations and motivates the exploration of alternative parameterizations of magnitude and orientation. This work forms part of the research program Model of General Quasi-Coherence (MGQC).
Author: Dominguez-Digat, Antonio
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7127596964