1. A Unified Topological Theory of Fermions, Bosons, and Hadrons via Rotational Dynamics. 2. A Geometric Theory of Particle Transformations: From Tori to Spheres and Half-Tori.

This paper presents a unified geometric model where elementary particles emerge as distinct topological phases of rotating contours. Fundamental principles include: (1) Two fixed points on the rotation axis define all states, (2) Fermions and bosonsrepresent boundary configurations (merged points and central axis alignment), (3) Quarks arise as oscillation modes between these states, (4) Gravitons mediate transitions as asymmetric ”half-torus” structures. The model explains quantum num-bers, confinement, and predicts new decay channels with graviton emission. TikZ diagrams illustrate particle transformations and hadronic structure. This paper presents a novel geometric model of elementary particles where fermions are represented as toroidal structures (tori),bosons as spherical structures, and gravitons as half-torus configurations. The model provides a unified topological interpretationof quantum numbers such as spin and charge. We describe three fundamental transformation processes between these geometric configurations, explaining particle annihilation, decay, and asymmetric transformations. The geometric approach offers new insights intoquantum gravity and the relationship between fermions and bosons.