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Review . 2026
License: CC BY
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Gravity as a Projection into S4: Derivation of the Hierarchy from Geometric Volume Suppression

Authors: Fabian, Dante;

Gravity as a Projection into S4: Derivation of the Hierarchy from Geometric Volume Suppression

Abstract

Gravity is uniquely weaker than the Standard Model forces by 34 orders of magnitude. In the Operator-Derived Dimension (ODD) framework, this hierarchy is a geometric consequence of projecting a 5D bulk onto a 4D hypersphere (S4). While gauge forces are confined to the intersection seam (N = 3), gravity propagates through the full encapsulating bulk volume (N = 4).We derive Newton’s constant G explicitly from the bulk curvature scale k and the anchor mass Manchor ≈ 173 GeV. The hierarchy arises from an exponential volume suppression factor e−S4 , where S4 is the geometric action of the hypersphere. We calculate that a geometric action of S4 ≈ 78 naturally reproduces the observed Planck scale (G ∼ 10−39 GeV−2) from the electroweak scale, unifying gravity with the Standard Model geometry.

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average
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