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| Format: | Recurso digital |
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Zenodo
2026
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| Matèries: | |
| Accés en línia: | https://doi.org/10.5281/zenodo.20159975 |
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- <p><strong>Version 3:</strong> </p> <p>This version further refines the methodological foundations of the MGQC framework by incorporating the mature interpretational developments of the program concerning structural persistence, effective projection, and restricted observability. The exposition has been expanded to clarify the coexistence of numerical systems as representational regimes, the non-destructive interpretation of mathematical operations, and the distinction between observable outputs and antecedent structural states.</p> <p>The article also strengthens the methodological role of quasi-numeric structures as layered representational frameworks involving admissible objects, state spaces, support structures, visibility or projection mechanisms, and external coherence conditions.</p> <p>The central methodological thesis of the article and its role within the MGQC research program remain unchanged, while the revised formulation provides a more coherent ontological and representational interpretation of collapse, projection, and structural accessibility.</p> <p><strong>Abstract</strong></p> <p><span>This article develops a revised methodological framework for the construction, stabilization, and interpretation of new numerical systems within the Generalized Multi-Geometric Quasi-Coherence (MGQC) research program. The revised formulation preserves the original layered methodological architecture while integrating the mature doctrinal developments of the MGQC concerning structural persistence, effective projection, restricted observability, representational coexistence, and operational non-destruction. The article argues that numerical systems should be interpreted not as mutually exclusive ontological replacements, but as layered representational regimes preserving different forms of structural accessibility. Within this interpretation, classical systems such as the natural numbers, integers, rational numbers, real numbers, complex numbers, and quaternionic structures remain fully legitimate within their operational domains while richer frameworks preserve additional orientational, contextual, compositional, and coherence-related structure. The revised framework further clarifies that mathematical operations do not destroy antecedent mathematical entities. Instead, operations establish relational projections and observable structures inside formal representational systems. This reinterpretation extends directly to quasi-numeric structures, where effective scalar outputs do not exhaust the total antecedent structure of quasi-states. The article also reformulates collapse as effective projection under observability restriction rather than ontological elimination or structural annihilation. The quasi-numeric proposal continues to serve as a methodological case study illustrating how enriched mathematical systems emerge through layered articulation involving admissible objects, ambient state spaces, operations, support structures, projection mechanisms, visibility conditions, and external coherence regimes. The resulting framework proposes a broader interpretation of mathematics as a hierarchy of coexistive representational systems preserving different forms of structural observability.</span></p> <p>This preprint forms part of the <strong>Model of General Quasi-Coherence (MGQC) </strong>research program.<br>The author publishes under the name Antonio Dominguez-Digat. Earlier records may appear under Antonio Domínguez, Antonio Dominguez, or Antonio Dominguez Digat.</p>