A closed spherical boundary is selected from the equality case of the isoperimetric inequality, A³ = 36π V². The Stefan–Boltzmann law on a sphere yields a dimensionless normalization equal to π³/15. Writing this normalization as a boundary condition, Λ R² = π³/15, fixes the scale of the sphere. Resolving the same surface into N Planck cells, A = N ℏG/c³, then yields an algebraic expression for the gravitational constant: G = 4π⁴c³/(15 ℏΛN). The argument is layered: geometry selects the sphere, the radiative law fixes the boundary normalization, and Planck-area counting closes the surface. In this form, the gravitational constant appears not as an independent input but as the algebraic closure of a spherical boundary construction.