Geometric Origin of the Proton-Electron Mass Ratio and the Resolution of the Hierarchy Problem via (2,2) Phase Space Volumetrics

The proton-to-electron mass ratio (μ ≈ 1836.15) and the extreme weakness of gravity relativeto electromagnetism (FG/FEM ≈ 10−40) are two of the most significant puzzles in the StandardModel. Conventionally, these are treated as arbitrary empirical parameters. In this letter, wepropose a unified topological derivation based on a split-signature (2, 2) spacetime manifold. Wedemonstrate that the proton represents a saturated phase space vortex with hexagonal locking,yielding a mass ratio of μ = 6π5 ≈ 1836.11 (99.998% precision). Furthermore, we resolve theHierarchy Problem by defining gravity not as a weak force, but as a geometrically diluted tensionacting on the entire metric volume, whereas electromagnetism is confined to topological knots. Thissuggests that fundamental constants are intrinsic geometric properties of the vacuum topology.