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Gaussian Splatting (GS) has demonstrated impressive quality and efficiency in novel view synthesis. However, shape extraction from Gaussian primitives remains an open problem. Due to inadequate geometry parameterization and approximation, existing shape reconstruction methods suffer from poor multi-view consistency and are sensitive to floaters. In this paper, we present a rigorous theoretical derivation that establishes Gaussian primitives as a specific type of stochastic solids. This theoretical framework provides a principled foundation for Geometry-Grounded Gaussian Splatting by enabling the direct treatment of Gaussian primitives as explicit geometric representations. Using the volumetric nature of stochastic solids, our method efficiently renders high-quality depth maps for fine-grained geometry extraction. Experiments show that our method achieves the best shape reconstruction results among all Gaussian Splatting-based methods on public datasets.