The 59-Dimensional Geometric Theory of Elementary Particle Masses

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 D_total = 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) = [E_Planck × 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.