What question did this study set out to answer?

This research aims to present a theoretical framework explaining the rest masses of elementary particles through a 59-dimensional geometric structure.

May 9, 2026Open Access

The 59-Dimensional Geometric Theory of Elementary Particle Masses

Key Points

This research aims to present a theoretical framework explaining the rest masses of elementary particles through a 59-dimensional geometric structure.
Introduced a 59-dimensional geometry combining M-theory, Calabi-Yau compactification, and SO(8) symmetry.
Verified the framework against data from 28 known elementary particles, comparing calculated masses to Particle Data Group values.
Formulated a master equation linking Planck-scale energy with the Riemann zeta function's zeros for mass predictions.
Achieved an average mass discrepancy of 0.009% against established particle data.
Calculated Newton's gravitational constant G with 0.00001% accuracy from Planck-scale quantities.
Predicted new particle masses testable in future colliders, addressing the baryon asymmetry problem.

Abstract

This paper introduces a speculative theoretical framework — the 59-Dimensional Geometric Theory — proposing that the rest masses of elementary particles are not arbitrary constants but emergent quantities arising from the folding of a structured 59-dimensional spacetime geometry. The 59-dimensional framework is constructed from three well-established components of modern theoretical physics: • 11 dimensions of M-theory (Witten, 1995) • 6 dimensions of Calabi-Yau compactification (superstring theory) • 8 dimensions of SO (8) Triality symmetry (unique to SO (8) ) giving Dₜotal = 11 + (6 × 8) = 59. The central master equation links Planck-scale energy to the first three non-trivial zeros of the Riemann zeta function (t1 = 14. 134, t2 = 21. 022, t3 = 25. 010), with a particle-specific geometric index n: m (n) = EPlanck × t1 × t2 × t3 / exp (59 + n) × t1^ (1/π) This single equation is verified against 28 known elementary particles — baryons, mesons, weak bosons, the Higgs boson, leptons, and quarks — yielding an average discrepancy of 0. 009% against Particle Data Group (2022) values. The framework further: • Generalizes Einstein's mass-energy relation E = mc² by providing a geometric origin for m • Derives Newton's gravitational constant G from Planck-scale quantities with 0. 00001% accuracy • Offers a geometric interpretation of the baryon asymmetry problem (matter/antimatter imbalance) based on the odd-prime nature of 59 • Predicts undiscovered particles at specific masses testable at LHC and future colliders The geometric index n is found to cluster around values directly connected to Riemann zeta zeros and the fine-structure constant, with baryons at n ≈ - (t1-t2-α) ≈ -7 (G2 manifold geometry) and weak bosons at n ≈ - (t1+t2) /π ≈ -11 (full M-theory geometry). This work is presented as a speculative hypothesis requiring peer review. It is submitted for scientific discussion, independent verification, and experimental testing. Priority is established by this deposit. Author: Ahmouri Abdelilah — Independent Researcher, Issoire, France, 2026.

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