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 the
Hierarchy Problem of the Standard Model. We propose that this disparity is not intrinsic but
geometric. By modeling the vacuum as a (2, 2) split-signature manifold, we demonstrate that gravity
acts as a global tension on the entire causal horizon volume (VH), while electromagnetism is confined
to the local phase space volume of topological defects (Vp). The hierarchy ratio emerges naturally
from the ratio of these characteristic volumes, Γ = VH/Vp ∼ 1040, without requiring fine-tuning or
supersymmetry.