The Forced Electron: A Rigorous Derivation of the Ground State Fermion and its Geometric Mass in the ODD Framework
Year: 2026
Type: preprint
Abstract: In the Standard Model, the electron’s mass and quantum numbers are axiomatic inputs. In the Operator-Derived Dimension (ODD) framework, we prove they are necessary geometric consequences. We begin with a foundational postulate: the vacuum is defined by the intersection of three rotating 4-dimensional hyperspheres. This geometry uniquely fixes the topological index (μ = 2) of a Transverse Projection Operator ˆQ. We provide a deductive proof that the stability of this operator forces the existenceof a ground state with the exact quantum numbers of the electron (spin-1/2, charge, statistics). Furthermore, we demonstrate that the electron’s mass emerges not from an arbitrary coupling, but as a geometric phase resonance (Φe ≈ 8.103) of the bulk anchor scale (kUV ≈ 173 GeV), governed by the universal hyperspherical projection law. All derivations are explicitly provided in the Appendix.
Author: Fabian, Dante
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7128495671
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