On the Axioms of Quasi-Magnitude and Coherent Collapse
Dominguez-Digat, Antonio
Abstract
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 This article develops an axiomatic framework for quasi-magnitude and coherent collapse, addressing the status of magnitude prior to its realization as a real number. Classical mathematics typically treats magnitude as a fully realized scalar property, but such treatment presupposes a collapse that suppresses orientational and latent structure. We formalize a pre-collapsed domain composed of infinitely many quasi-states, introduce quasi-magnitude as a primitive carrier of potential magnitude, and define collapse as a surjective and irreversible operator mapping quasi-magnitudes to real values. Within this framework, classical notions such as sign, absolute value, order, and commutativity arise as emergent operators rather than primitive features. The real line is thereby characterized as a maximally restricted limit structure within a broader quasi-numerical hierarchy. This preprint forms part of the Model of General Quasi-Coherence (MGQC) research program.The author publishes under the name Antonio Dominguez-Digat. Earlier records may appear under Antonio Domínguez, Antonio Dominguez, or Antonio Dominguez Digat.