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The research aims to derive fundamental constants and the mass spectrum of the Standard Model using a unified field theory based on F-Theory.

March 13, 20260 citationsOpen Access

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JOJoshua E Osborne

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The research aims to derive fundamental constants and the mass spectrum of the Standard Model using a unified field theory based on F-Theory.
Utilized a Calabi-Yau threefold as a degree 18 hypersurface in weighted projective space.
Applied D-brane intersections to establish relationships between global volume and local topology.
Developed a computational protocol for deriving mass constants, including electron and proton mass.
Used theoretical constructs like the Ray-Singer Torsion and Mirror Symmetry for proofs.
Electron mass derived as approximately 0.511 MeV, proton mass as 938.27 MeV.
Neutrino mass established between 0.05 and 0.07 eV via the Type I See-Saw Mechanism.
Identified QCD Axion with a decay constant of approximately 8.27×10^13 GeV and mass of 0.5 μeV.
Proved existence of exactly three generations of fermions through intersection matrix equations.

Abstract

It presents a zero-parameter unified field theory that derives the fundamental constants and the Standard Model mass spectrum directly from the topology of F-Theory compactification. By utilizing a Calabi-Yau threefold defined as a degree 18 hypersurface within the weighted projective space, this framework eliminates continuous free parameters and empirical fitting. The mathematical proofs demonstrate the exact topological tension between the global volume required for the hierarchy problem and the local topology required for the Standard Model, resolving it via D-brane intersections. Key Derivations Included: Electron Mass (me): Derived via volume suppression (≈0.511 MeV. Proton Mass (mp): Derived via Holographic QCD throat ratios (≈938.27 MeV. Neutrino Mass (mν): Derived via the Type I See-Saw Mechanism natively within the string geometry (≈0.05−0.07 eV). Dark Matter (Axion): Identifies the QCD Axion with a decay constant fa≈8.27×1013 GeV and mass ma≈0.5 μeV, falling exactly into the Anthropic Axion Window. Fermionic Generations: Proves the existence of exactly 3 generations of matter via the intersection matrix equation and Spin(8) Triality automorphisms. Methodological Framework: The repository outlines the "Triple-Lock Mechanism" which locks the Racetrack W0 via Ray-Singer Torsion, the Volume V via the Euler characteristic (χ=−3192), and the Yukawa Ye via the local matter metric. To bypass the unknown local metric, the proofs utilize Mirror Symmetry and the Bershadsky-Cecotti-Ooguri-Vafa (BCOV) Holomorphic Anomaly Equations. Also included is the executable 6-step computational protocol (compatible with SageMath/Macaulay2) detailing the Diophantine search: Toric Initialization & Mori Cone Extraction GKZ Hypergeometric System (Picard-Fuchs Operators) Mirror Map & Genus-0 Gopakumar-Vafa (GV) Invariants BCOV Anomaly Integration for Genus-1 GV Invariants Diophantine Flux Lattice Shift (Anomaly-free state generation) Ratio Convergence of the Ray-Singer Torsions This is a theoretical mathematics and computational physics preprint establishing foundational prior art.

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