The Geometric Dilution of Gravity: A Topological Resolution to the Hierarchy Problem via (2,2) Split-Signature Volumetrics

The extreme weakness of gravity relative to electromagnetism (approx. 10−40) constitutes theHierarchy Problem of the Standard Model. We propose that this disparity is not intrinsic butgeometric. By modeling the vacuum as a (2, 2) split-signature manifold, we demonstrate that gravityacts as a global tension on the entire causal horizon volume (VH), while electromagnetism is confinedto the local phase space volume of topological defects (Vp). The hierarchy ratio emerges naturallyfrom the ratio of these characteristic volumes, Γ = VH/Vp ∼ 1040, without requiring fine-tuning orsupersymmetry.