Z'Mathemathical Foundation on perceptual collapse
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| Natura: | Recurso digital |
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Zenodo
2025
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| _version_ | 1866902140368191488 |
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| author | Cicero, Ollivier |
| author_facet | Cicero, Ollivier |
| contents | <p>This article presents the Z′ model, a formal mathematical framework for perceptual collapse based on category theory, modal logic, and relational algebra. The model defines a dynamic tension field Λ(x, Pv) modulated by a point of view Pv, and a sigmoidal collapse operator ℓ(x, Pv) that governs perceptual emergence. The formal system includes modal operators (□ₙ, ◇ₙ), a non-commutative algebra of perceptual transitions, and a cartesian closed category _{Z′} describing the structure of resolved states. Unlike the Z(n) model which embeds collapse into physical curvature, Z′ focuses on the abstract logic of perception. It provides the categorical and logical skeleton from which the Z(n) model emerges, enabling a unified theory linking quantum, cognitive, and physical processes.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_16739860 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Z'Mathemathical Foundation on perceptual collapse Cicero, Ollivier perceptual collapse, modal logic, category theory, relational field, cognitive emergence, non-commutative algebra, tension dynamics, quantum cognition, viewpoint modulation, Z′ model, Λ field, structured observation <p>This article presents the Z′ model, a formal mathematical framework for perceptual collapse based on category theory, modal logic, and relational algebra. The model defines a dynamic tension field Λ(x, Pv) modulated by a point of view Pv, and a sigmoidal collapse operator ℓ(x, Pv) that governs perceptual emergence. The formal system includes modal operators (□ₙ, ◇ₙ), a non-commutative algebra of perceptual transitions, and a cartesian closed category _{Z′} describing the structure of resolved states. Unlike the Z(n) model which embeds collapse into physical curvature, Z′ focuses on the abstract logic of perception. It provides the categorical and logical skeleton from which the Z(n) model emerges, enabling a unified theory linking quantum, cognitive, and physical processes.</p> |
| title | Z'Mathemathical Foundation on perceptual collapse |
| topic | perceptual collapse, modal logic, category theory, relational field, cognitive emergence, non-commutative algebra, tension dynamics, quantum cognition, viewpoint modulation, Z′ model, Λ field, structured observation |
| url | https://doi.org/10.5281/zenodo.16739860 |