On the Axioms of Quasi-Magnitude and Coherent Collapse

Version 3: This version clarifies the sectorial status of collapse, refines the treatment of emergent operators such as sign and absolute value, and incorporates a brief distinction between the fundamental collapse rule and a continuous auxiliary orientation index, while preserving the article’s central axiomatic 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. The present framework formalizes a pre-collapsed domain composed of infinitely many quasi-states, introduces quasi-magnitude as a primitive carrier of potential magnitude, and defines collapse as a surjective, irreversible, and sectorial 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 article also distinguishes the sectorial resolution of collapse from any auxiliary continuous measure of orientational tendency: such an index may describe graded sign-tendency prior to collapse, but it does not define the collapse rule itself. 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.