Prediction of the Triply Charmed and Triply Bottom Baryons

Title: Prediction of the Triply Charmed and Triply Bottom Baryons Ω₂₂₂^++ and Ω₁₁₁^-- from a Discrete Elastic Tetrahedral Mesh Authors: Alex Bertran Description / Abstract: In March 2026, the LHCb collaboration announced the observation of the doubly charmed baryon Ξ₂₂^+. Its mass, around 3620 MeV/c², is now an experimental fact. But why that mass? Why these combinations? In the standard description, quark masses are free parameters. In the Mesh framework, they are not. The Cosmic Mesh is a closed, self‑similar, Face‑Centered Cubic (FCC) lattice of unbreakable elastic tetrahedra at the Planck scale. Each tetrahedron can twist in discrete steps of 120°, and the resulting torsional entanglement defines a local strain Sᵢ. A single deterministic rule governs all motion: a vibration moves at each step to the neighboring tetrahedron that maximizes the entanglement gradient. No probability. No collapse. Just deterministic motion in a discrete lattice. Particles are standing waves trapped in topological knots. Quarks are specific vibrational modes in small knots. Baryons are stable triplets of colored knots (red, green, blue) that mutually stabilize via the migration rule. Using only the geometric origin of the fine‑structure constant (α⁻¹ = 135 + 2πφ/5) and the same dragging correction ε = 1/169 ≈ 0. 005917 derived from the fundamental 13‑cluster (1 central tetrahedron + 12 neighbors), we predict: Ω₂₂₂^++ (triply charmed) ≈ 4950 MeV/c² (range 4870–5070 MeV/c²) Ω₁₁₁^-- (triply bottom) ≈ 13420 MeV/c² (range 13120–13720 MeV/c²) Both predictions are falsifiable with LHCb Run 3/4 data. Their observation would confirm that particle masses are not arbitrary constants but emerge from the geometry and elasticity of spacetime itself. This preprint is a direct application of the framework developed in “THE BREATHING UNIVERSE: A Torsional Solid Machine” (Zenodo, 2026). It shows that the same mechanical principles that give the lepton masses, the fine‑structure constant, and the gravitational constant also predict new particles with no free parameters. Keywords: particle physics, baryons, exotic hadrons, LHCb, tetrahedral lattice, discrete spacetime, topological defects, mass prediction, quark model, emergent particle masses, triply charmed baryon, triply bottom baryon, golden ratio, 13‑cluster License: Creative Commons Attribution 4. 0 International (CC BY 4. 0) Related works: Bertran, A. (2026). THE BREATHING UNIVERSE: A Torsional Solid Machine. Zenodo. Bertran, A. , Jussà, E. , Vila, M. (2025). The Universe's Geometric Inertia – The Jussà-Vila Ansatz. Zenodo. Bertran, A. (2026). The End of the Copenhagen Interpretation: Einstein Was Right — Reality Is Local, Deterministic, and Made of a Discrete Elastic Mesh. Zenodo. Updates: Update v1: "Stiffness matrix eigenvalues" suppressed. Pure geometric origin for α⁻¹