The Geometry of Spacetime Quanta: Resolving the Radius, Packing, and Expansion Paradoxes in the SV0 Framework

In this paper (Paper XLVI of the SV0 series), we address three fundamental geometric paradoxes that arise when modeling the discrete building blocks of spacetime as "Spacetime Quanta". First, the Diameter Paradox: if a quantum has a radius of the Planck length (r = ℓ_Pl), its diameter is 2ℓ_Pl, conflicting with the notion that ℓ_Pl is the absolute minimum length. Second, the Packing Paradox: if quanta are modeled as spheres, packing them leaves unavoidable gaps. Third, the Expansion Paradox: if spacetime is already 100% filled with discrete quanta, how can new quanta be created during cosmic expansion without requiring pre-existing empty space? We resolve all three paradoxes by demonstrating that Spacetime Quanta are not geometric spheres, but abstract topological nodes in a dynamical lattice. We define the fundamental length scale by effective volume ℓ_Pl³, eliminating the diameter paradox. Using Voronoi tessellations and spin network topology, we show that space is perfectly gapless (resolving the packing paradox). Finally, we show that expansion occurs via topological graph moves and the conversion of the negative-volume sector (V_B) into new V_A quanta, eliminating the need for an external "container" of empty space.