On the Real Line as a Highly Restricted Structure

Version 2: This version corrects errors, improves exposition, and updates terminology and figures to better reflect the article’s scope, while preserving the original preprint’s central thesis and role within the MGQC research program. 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 orientation-bearing magnitude domain. Under this interpretation, the real line preserves magnitude only after suppressing orientational distinctions, thereby…