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2026
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| Online Access: | https://doi.org/10.5281/zenodo.19363390 |
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| _version_ | 1866901221308104704 |
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| author | EBIHARA, GOU |
| author_facet | EBIHARA, GOU |
| contents | <p>【英語版説明(v2)】<br>This paper presents FK-1 v2, the foundational work of the Biomimetic Control Engineering (FK Series), which integrates the entire Gamma Theory framework—V Series, SP Series, EX Series, and A/B Series—into a unified formal system. Part I establishes the mathematical foundations: the life mapping Γ = L·E·A, the dynamical equation of recognition temperature T_κ, the geometric proof of the triple-point critical value ε_c = Δ = |π/(3√3) − φ⁻¹|, and the identification of the integration constant C with Ay = 0_v as the source of evolutionary divergence. Part II constructs a nonlinear dynamical system of four variables—emotion κ, bodily expression Ay, internal gap Δ, and self-other boundary ℬ—and demonstrates the existence of a triple-point bifurcation corresponding to three qualitatively distinct states: normal, emotional oscillation, and emotional fixation. Social emotions such as shame, jealousy, empathy, and social stress are numerically reproduced under specific parameter conditions. FK-1 v2 serves as the foundational paper for the FK Series, providing a unified mathematical framework from the deepest structures of mathematics to the control of social emotions in living systems. This version incorporates peer review revisions including explicit definitions of the life mapping product operations, derivation of the recognition temperature equation from variational principles, a geometric proof of the triple-point critical value, and parameter sensitivity analysis for the social emotion model. DOI: 10.5281/zenodo.xxxxxxxx (to be assigned)</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19363390 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | FK-v2: Unified Formulation of Life Mapping and Social Emotions — Foundations of Biomimetic Control Engineering Based on Gamma Theory EBIHARA, GOU <p>【英語版説明(v2)】<br>This paper presents FK-1 v2, the foundational work of the Biomimetic Control Engineering (FK Series), which integrates the entire Gamma Theory framework—V Series, SP Series, EX Series, and A/B Series—into a unified formal system. Part I establishes the mathematical foundations: the life mapping Γ = L·E·A, the dynamical equation of recognition temperature T_κ, the geometric proof of the triple-point critical value ε_c = Δ = |π/(3√3) − φ⁻¹|, and the identification of the integration constant C with Ay = 0_v as the source of evolutionary divergence. Part II constructs a nonlinear dynamical system of four variables—emotion κ, bodily expression Ay, internal gap Δ, and self-other boundary ℬ—and demonstrates the existence of a triple-point bifurcation corresponding to three qualitatively distinct states: normal, emotional oscillation, and emotional fixation. Social emotions such as shame, jealousy, empathy, and social stress are numerically reproduced under specific parameter conditions. FK-1 v2 serves as the foundational paper for the FK Series, providing a unified mathematical framework from the deepest structures of mathematics to the control of social emotions in living systems. This version incorporates peer review revisions including explicit definitions of the life mapping product operations, derivation of the recognition temperature equation from variational principles, a geometric proof of the triple-point critical value, and parameter sensitivity analysis for the social emotion model. DOI: 10.5281/zenodo.xxxxxxxx (to be assigned)</p> |
| title | FK-v2: Unified Formulation of Life Mapping and Social Emotions — Foundations of Biomimetic Control Engineering Based on Gamma Theory |
| url | https://doi.org/10.5281/zenodo.19363390 |