A Determinant-Based Invariant Surface Framework for Complex Biological Systems

This work presents a framework based on the invariant sum of determinants, applied to complex biological systems. Matrices are constructed from a specific set of numbers whose determinants correspond to geometric surfaces. While individual determinants vary under defined transformations, the total sum remains constant, providing a mathematical tool for modeling stability and structural balance. The framework is relevant to fractal-like architectures in organs such as the brain, heart (myocardium), kidneys, and lungs, linking mathematical invariance with biological form and stability.