A Geometric Consistency Bound for the Exclusion Parameter Π = 1/4 in ℝ³: Admissibility under the Kepler Void Fraction

We study a limited geometric consistency question for an effective excluded-volume parameter Π in three spatial dimensions. Using the Kepler packing theorem (proved by Hales), we take the complementary void fraction v_void = 1 - π/(3√2) ≈ 0.25952 as a geometric ceiling under a packed-sphere substrate interpretation. We then adopt the model-dependent admissibility condition Π ≤ v_void, where Π is treated as a coarse-grained effective exclusion parameter rather than the geometric porosity itself. A companion closure proposes the dimensional family Π(D) = 1/(D+1), whose three-dimensional member is Π(3) = 1/4. Restricting attention to the associated unit-fraction family, we show that 1/4 is the largest admissible unit fraction below the Kepler void ceiling, whereas 1/3 is not. The result is conditional and does not derive Π=1/4 from packing theory alone; it establishes a limited geometric consistency bound for the three-dimensional case.