What question did this study set out to answer?

The research aims to introduce a topological constant that governs tipping points in biological and technical clusters, revealing new phases of understanding in these systems.

March 1, 2026Open Access

Systemic Bio- and Neurophysics

Key Points

The research aims to introduce a topological constant that governs tipping points in biological and technical clusters, revealing new phases of understanding in these systems.
Introduced the Gemini Constant to define tipping points in hexagonal clusters.
Applied Change-Point Analysis to various datasets including neural and avian systems.
Provided mathematical derivation of the Gemini-Logit Filter and included R-code for validation.
Demonstrated that phase transitions are determined by geometric constraints rather than randomness.
Found consistent patterns across diverse datasets, supporting the universality of the Gemini Constant.

Abstract

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.

Systemic Bio- and Neurophysics

Key Points

Abstract

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