On the Axioms of Quasi-Magnitude and Coherent Collapse

Version 4: This version consolidates the axiomatic framework of quasi-magnitude and coherent collapse within the MGQC model by integrating a non-destructive interpretation of collapse as effective projection under restricted observability. It clarifies the distinction between ontological persistence and observational indistinguishability, refines the role of structural fibers, orientational tension, and emergent scalar operators, and stabilizes the doctrinal relation between coherent collapse and effective projection. The revision also expands the formal treatment of quasi-states, quasi-zero, and representational reduction, while preserving the article’s foundational axiomatic structure and its role within the Model of Generalized Quasi-Coherence (MGQC).

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 representational transition in which orientational and latent structure are not distinguished in the scalar image. The framework formalizes a pre-projection domain composed of infinitely many quasi-states, introduces quasi-magnitude as a primitive carrier of potential magnitude, and defines coherent collapse as a surjective, non-injective, and sectorially sign-resolving map from quasi-magnitudes to real values.
Within this framework, classical notions such as sign, absolute value, order, and commutativity arise as emergent operators or induced features of the collapsed scalar regime rather than as primitive features of magnitude itself. In continuity with earlier articles in the series, the present framework also distinguishes the sectorial resolution of coherent collapse from a continuous auxiliary orientation index associated with the internal parameter θ. That index may describe graded signed tendency prior to projection, but it does not define the projection rule itself.
The article is aligned with the Model of Generalized Quasi-Coherence (MGQC), especially with the principles of structural persistence, non-destructive representation, restricted observability, coexistence of representational regimes, and the distinction between antecedent state and observable scalar image. The real line is thereby characterized as a maximally restricted scalar regime within a broader quasi-numerical hierarchy. The article is foundational and axiomatic in scope: it does not yet define a complete algebra of quasi-numbers, but supplies the conceptual and formal basis for such developments.

This preprint forms part of the Model of Generalized 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.