The inevitability of various particle masses for hadrons, quarks, leptons, atoms, biological molecules, liquid droplets of fossil fuel and water, living cells including microorganisms and cancers, multi-cellar systems such as organs, neural systems, and the brain, stars, galaxies, and the cosmos is synthetically revealed. This is possible because each flexible particle is commonly generated by a mode in which a larger particle breaks up into two smaller ones through a gourd shape with two lumps. These masses, sizes, frequencies, and diversity dominated by super-magic numbers including the silver ratio, in fractal nature can be derived by the fusion of the quasi-stability principle defined between absolute instability and neutral stability, the indeterminacy principle extended for quantum, statistical, and continuum mechanics, and the spherical Lie group theory. The analyses also result in a new mathematical definition of living beings and non-living systems and further explain the standard network patterns of various particles and also the relation between information, structure, and function, because the proposed theory based on gourds posits a new hyper-interdisciplinary physics that explains a very wide range of scales, while the Newton, Schrödinger, and Boltzmann equations describe only a narrow range of scales.
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