We investigate whether discrete four-dimensional geometric structures can give rise to stable, dimensionless ratios independently of any assumed dynamics. Within the Origin Geometry (OG) framework, we analyze purely static invariants of regular discrete four-dimensional cells under coarse-graining to an effective three-dimensional description. By identifying boundary faces as the natural carriers of geometric flux and interaction capacity, we show that nontrivial dimensionless ratios emerge as intrinsic structural properties of highly isotropic four-dimensional geometries, with the 600-cell serving as a representative polytope. These ratios arise from geometry alone and do not rely on field equations, quantization procedures, renormalization schemes, or fitted parameters. The results suggest that certain dimensionless constraints observed in effective physical theories may reflect pre-dynamical geometric invariants rather than parameters fixed by specific interactions. This work establishes a geometric baseline upon which dynamical and physical interpretations may be constructed in subsequent studies.
The Duy Tan Truong (Thu,) studied this question.