Torsion Tubes, Orbifold Geometry, and Symmetry Restoration in Hadronic Triplets

We present a unified geometric framework connecting torsion flux tubes, orbifold factorization, and Koide relations for both baryonic and mesonic triplets. Fermions are modeled as tori T 2 whose Z3 symmetry breaking generates electric charge. Quark confinement arises from the Z3-orbifold structure T 2/Z3, where each quark corresponds to a sheet of the universal cover. Torsion tubes from earlier work areidentified as the spatial realization of this orbifold geometry. Mesons correspond to Z2-orbifolds T 2/Z2, with their triplets also exhibiting R ≈ 1/3 Koide ratios,indicating universal symmetry restoration through triplet projection. Gluon fields emerge as torsion gradients between orbifold sheets. The model provides a complete geometric description of confinement, hadron spectroscopy, and mass relations.