[STCT-PROJECTION] Algebraic Holographic Projection and Information Conservation via Rough Operator Algebra: Resolving the Dimensional Reduction Anomaly
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| Sprache: | Englisch |
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2026
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| _version_ | 1866901671286669312 |
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| author | Lee, Seonggil |
| author_facet | Lee, Seonggil |
| contents | <p>This paper resolves the long-standing problem of information loss and entropy divergence during the dimensional reduction (projection) of high-dimensional objects to lower dimensional manifolds, utilizing the framework of Rough Operator Algebra (ROA). Unlike traditional geometric projection theories that suffer from irreversible information deficits, this study introduces a topological phase transition within the Type III1 factor of von Neumann algebras. We rigorously prove that the geometric information ostensibly lost during the N →N−1projection is not destroyed; rather, it is perfectly encoded into the topological<br>time phase of the modular automorphism group, mediated by the Golden Ratio resonance frequency (ωφ). This mechanism not only establishes a new algebraic holographic principle that resolves the Hawking information paradox but also provides a concrete theoretical foundation for designing holographic outer shells in macroscopic spacetime engineering.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19995894 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | [STCT-PROJECTION] Algebraic Holographic Projection and Information Conservation via Rough Operator Algebra: Resolving the Dimensional Reduction Anomaly Lee, Seonggil Rough Operator Algebra(ROA) von Neumann Algebras Type III_1 Factor Connes Cocycle Derivative Modular Automorphism Group Tomita-Takesaki Theory Topological Phase Transition Holographic Principle Hawking Information Paradox Quantum Gravity Golden Ratio Resonance(ωφ) Seonggil Field Equations(SFE) Algebraic Holographic Projection Macroscopic Spacetime Engineering Holographic Shell Dimensional Reduction Anomaly Information Conservation Topological Entanglement Entropy <p>This paper resolves the long-standing problem of information loss and entropy divergence during the dimensional reduction (projection) of high-dimensional objects to lower dimensional manifolds, utilizing the framework of Rough Operator Algebra (ROA). Unlike traditional geometric projection theories that suffer from irreversible information deficits, this study introduces a topological phase transition within the Type III1 factor of von Neumann algebras. We rigorously prove that the geometric information ostensibly lost during the N →N−1projection is not destroyed; rather, it is perfectly encoded into the topological<br>time phase of the modular automorphism group, mediated by the Golden Ratio resonance frequency (ωφ). This mechanism not only establishes a new algebraic holographic principle that resolves the Hawking information paradox but also provides a concrete theoretical foundation for designing holographic outer shells in macroscopic spacetime engineering.</p> |
| title | [STCT-PROJECTION] Algebraic Holographic Projection and Information Conservation via Rough Operator Algebra: Resolving the Dimensional Reduction Anomaly |
| topic | Rough Operator Algebra(ROA) von Neumann Algebras Type III_1 Factor Connes Cocycle Derivative Modular Automorphism Group Tomita-Takesaki Theory Topological Phase Transition Holographic Principle Hawking Information Paradox Quantum Gravity Golden Ratio Resonance(ωφ) Seonggil Field Equations(SFE) Algebraic Holographic Projection Macroscopic Spacetime Engineering Holographic Shell Dimensional Reduction Anomaly Information Conservation Topological Entanglement Entropy |
| url | https://doi.org/10.5281/zenodo.19995894 |