On the Missed Structures Beyond the Real Line

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 provides a complete and internally consistent representation of magnitude under linear order; however, this completeness may be achieved through a strong structural restriction. Under the interpretive framework adopted here, the real line may be read as preserving only two extreme orientational outcomes, thereby identifying a richer directional continuum with a rigid linear model. The present article makes explicit some of the structures suppressed by this…