Zero as Emergent Topological Interface: Formal Framework and Residue Pairing.
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| Format: | Recurso digital |
| Langue: | anglais |
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2025
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| _version_ | 1866901675347804160 |
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| author | Medford, Zachary |
| author_facet | Medford, Zachary |
| contents | <p><strong>This paper potentially introduces a novel framework in which zero is not treated as a passive scalar but as a topological interface embedded within emergence geometry. </strong></p> <p><strong>This framework is a work in progress that we have strong confidence in. We welcome collaboration and further refinements to strengthen or falsify the theorems.</strong></p> <p>Drawing from collapse mechanics, information theory, and quantum topology, the paper proposes that <strong>zero operates as a phase boundary, a singularity in the emergence manifold where opposing potentialities converge, fold, and cancel</strong>. This structure enables a new class of decoherence models, collapse criteria, and information-theoretic thresholds, with implications for both quantum field behavior and categorical boundary logic.</p> <p>The framework integrates spinor-based collapse loops, entropy-phase coupling, and dual-zero symmetry breaking to establish a formal role for zero in structured emergence. Simulation models, symbolic terrain maps, and cross-domain analogues (including cognitive and computational parallels) are presented.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_15560946 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Zero as Emergent Topological Interface: Formal Framework and Residue Pairing. Medford, Zachary topological collapse, zero singularity, real blow-up, quantum geometry, spinor interface, anti-holomorphic involution, emergence theory, KR-theory, T-duality, categorical topology, orbifold geometry, residue pairing, decoherence structure, conformal anomalies, structured collapse, phase singularity <p><strong>This paper potentially introduces a novel framework in which zero is not treated as a passive scalar but as a topological interface embedded within emergence geometry. </strong></p> <p><strong>This framework is a work in progress that we have strong confidence in. We welcome collaboration and further refinements to strengthen or falsify the theorems.</strong></p> <p>Drawing from collapse mechanics, information theory, and quantum topology, the paper proposes that <strong>zero operates as a phase boundary, a singularity in the emergence manifold where opposing potentialities converge, fold, and cancel</strong>. This structure enables a new class of decoherence models, collapse criteria, and information-theoretic thresholds, with implications for both quantum field behavior and categorical boundary logic.</p> <p>The framework integrates spinor-based collapse loops, entropy-phase coupling, and dual-zero symmetry breaking to establish a formal role for zero in structured emergence. Simulation models, symbolic terrain maps, and cross-domain analogues (including cognitive and computational parallels) are presented.</p> |
| title | Zero as Emergent Topological Interface: Formal Framework and Residue Pairing. |
| topic | topological collapse, zero singularity, real blow-up, quantum geometry, spinor interface, anti-holomorphic involution, emergence theory, KR-theory, T-duality, categorical topology, orbifold geometry, residue pairing, decoherence structure, conformal anomalies, structured collapse, phase singularity |
| url | https://doi.org/10.5281/zenodo.15560946 |