Introduces the Gemini Constant for analyzing phase transitions in biological and technical systems, suggesting new insights into their deterministic nature.
This paper introduces a universal topological constant, the Gemini Constant (ϕG≈0.5714), which defines the deterministic tipping point in hexagonal (k=7) biological and technical clusters. By applying Change-Point Analysis to diverse datasets—from neural columns to avian swarms—we demonstrate that phase transitions are not stochastic but governed by geometric constraints. We provide the mathematical derivation (Gemini-Logit Filter) and R-code for verification.
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Rudolf Schaefer (2026) studied this question.
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