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2026
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| Accesso online: | https://doi.org/10.5281/zenodo.19226356 |
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| _version_ | 1866902091442683904 |
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| author | Israel M. Rafaelovich |
| author_facet | Israel M. Rafaelovich |
| contents | <p dir="auto"><strong>Abstract:</strong> We develop a formal framework that classifies all modes of information loss under gauge reduction into exactly three non-symmetric types: the Jumping Edge (geometric annihilation under canonical projection), Capture Points (translational untranslatability), and the Orbital Cycle K (dynamical orbital collapse). These types are unified by a single Obstruction Functional : F → {0,1}. We prove the completeness of the classification (every mode of information loss belongs to exactly one of the three types) and show that the orbital type K serves as the dynamical organizing principle generating both (via Z/2-monodromy) and (via orbit order p−1) in the concrete model p=11, g=2. All rigorous mathematical results are stated for this model; generalizations and boundary conditions appear in §5. Physical interpretations (aromatic stability and discrete-continuous language models) are strictly separated from the mathematics in §7.</p> <p dir="auto">This preprint introduces the Gauge Completion Principle as a new topological invariant of gauge reduction.</p> <p dir="auto"><strong>Version:</strong> 2.1 <strong>Date:</strong> 25 March 2026 <strong>Author:</strong> Israel M. Rafaelovich, Independent Researcher, Kiriat Arba, Israel</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19226356 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
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| spellingShingle | Hidden Objects under Gauge Reduction: A Complete Classification via the Obstruction Functional Israel M. Rafaelovich gauge reduction, hidden objects, obstruction functional, jumping edge, capture points, orbital cycle, monodromy, gauge completion principle, aromatic stability, topological classification <p dir="auto"><strong>Abstract:</strong> We develop a formal framework that classifies all modes of information loss under gauge reduction into exactly three non-symmetric types: the Jumping Edge (geometric annihilation under canonical projection), Capture Points (translational untranslatability), and the Orbital Cycle K (dynamical orbital collapse). These types are unified by a single Obstruction Functional : F → {0,1}. We prove the completeness of the classification (every mode of information loss belongs to exactly one of the three types) and show that the orbital type K serves as the dynamical organizing principle generating both (via Z/2-monodromy) and (via orbit order p−1) in the concrete model p=11, g=2. All rigorous mathematical results are stated for this model; generalizations and boundary conditions appear in §5. Physical interpretations (aromatic stability and discrete-continuous language models) are strictly separated from the mathematics in §7.</p> <p dir="auto">This preprint introduces the Gauge Completion Principle as a new topological invariant of gauge reduction.</p> <p dir="auto"><strong>Version:</strong> 2.1 <strong>Date:</strong> 25 March 2026 <strong>Author:</strong> Israel M. Rafaelovich, Independent Researcher, Kiriat Arba, Israel</p> |
| title | Hidden Objects under Gauge Reduction: A Complete Classification via the Obstruction Functional |
| topic | gauge reduction, hidden objects, obstruction functional, jumping edge, capture points, orbital cycle, monodromy, gauge completion principle, aromatic stability, topological classification |
| url | https://doi.org/10.5281/zenodo.19226356 |