On the Real Line as a Highly Restricted Structure

Version 3: This version clarifies the distinction between the fundamental collapse of linear representation and a continuous auxiliary orientation index, while preserving the article’s central thesis and its role within the MGQC research program. It also refines the exposition of the real line as a structurally restrictive quotient image of a more expressive orientation-bearing magnitude domain. Abstract The real line is standardly treated as the canonical structure for the representation of continuous magnitude. This article proposes a different interpretation. Rather than taking ℝ as a primitive representational starting point, it examines the real line as a one-dimensional linear image of a more expressive…