Theoretical study analyzes six mutually tangent spheres at a common origin, highlighting heuristic connections to closed Friedmann cosmology and observational curvature constraints.
AbstractThis work is a direct sequel and three-dimensional generalization of [1], wherethe Planck resolution threshold lp was applied to the tangency of two circles. Here we replace the circles with six equal spheres of radius R centered on the coordinate axes, all tangent at a common origin O. Unlike the twodimensional case, neighboring (non-opposite) spheres intersect not in two points but along an entire circle. Separately, we discuss (as a heuristic analogy, not a physical derivation) the connection between the idea that “space exists only within a finite cell” and the closed (spherical) universe hypothesis ofFriedmann cosmology, and cite current observational curvature constraints.
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Oleksandr Danylov (2026) studied this question.
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