From Minimal Existence to Human Definition: The CES-IMU-HSG Theoretical Framework
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908594458329088 |
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| author | Itoh, Kei |
| author_facet | Itoh, Kei |
| contents | This study presents an inter-universal mathematical-logical framework constructed upon the minimal axiom Cogito, ergo sum (CES), integrating the Intermediate Meta-Universe (IMU) and the Hierarchical State Grid (HSG). The CES defines existence as a reflexive correspondence --'to be' and 'to be sayable'--and positions any formal system, including ZFC or HoTT, as an attachable extension atop this minimal structure. The IMU functions as a registry of axiomatic dependencies that connect heterogeneous theories, employing the Institution-theoretic framework to ensure coherent inter-theoretical linkages. The HSG concretizes these ideas through categorical construction, defined by three orthogonal axes: the state-depth axis, the mapping-hierarchy axis, and the temporal axis incorporating the principle of 'no future reference.' Through these, the identity of 'definition = state' is formally established as a categorical property. Extending this structure to biological systems, the neural system is implemented as a 0-3D complex of neuron-function fields on the HSG, while its categorical extensions via fiberization over the material base enable the parallel integration of multiple physiological universes-neural, endocrine, learning, genetic, and input/output systems-into a coherent adjoint ensemble. Within this framework, human behavior and cognition emerge as temporal compositions of inter-universal algorithms constrained by the material base. Finally, by contrasting human cognition, which relies on external CES, with machine existence, this study introduces the concept of internal CES, wherein a machine grounds its own logic upon the factuality of its operation. This internal self-axiomatization establishes a continuous bridge between philosophical ontology and engineering implementation, providing a new foundation for the autonomous and self-defining existence of artificial intelligence. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_13400 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | From Minimal Existence to Human Definition: The CES-IMU-HSG Theoretical Framework Itoh, Kei Neural and Evolutionary Computing Artificial Intelligence Logic in Computer Science This study presents an inter-universal mathematical-logical framework constructed upon the minimal axiom Cogito, ergo sum (CES), integrating the Intermediate Meta-Universe (IMU) and the Hierarchical State Grid (HSG). The CES defines existence as a reflexive correspondence --'to be' and 'to be sayable'--and positions any formal system, including ZFC or HoTT, as an attachable extension atop this minimal structure. The IMU functions as a registry of axiomatic dependencies that connect heterogeneous theories, employing the Institution-theoretic framework to ensure coherent inter-theoretical linkages. The HSG concretizes these ideas through categorical construction, defined by three orthogonal axes: the state-depth axis, the mapping-hierarchy axis, and the temporal axis incorporating the principle of 'no future reference.' Through these, the identity of 'definition = state' is formally established as a categorical property. Extending this structure to biological systems, the neural system is implemented as a 0-3D complex of neuron-function fields on the HSG, while its categorical extensions via fiberization over the material base enable the parallel integration of multiple physiological universes-neural, endocrine, learning, genetic, and input/output systems-into a coherent adjoint ensemble. Within this framework, human behavior and cognition emerge as temporal compositions of inter-universal algorithms constrained by the material base. Finally, by contrasting human cognition, which relies on external CES, with machine existence, this study introduces the concept of internal CES, wherein a machine grounds its own logic upon the factuality of its operation. This internal self-axiomatization establishes a continuous bridge between philosophical ontology and engineering implementation, providing a new foundation for the autonomous and self-defining existence of artificial intelligence. |
| title | From Minimal Existence to Human Definition: The CES-IMU-HSG Theoretical Framework |
| topic | Neural and Evolutionary Computing Artificial Intelligence Logic in Computer Science |
| url | https://arxiv.org/abs/2510.13400 |