Geometric Calculation of Hadron Masses \\ Solution of the Three-Body Problem (without using strong interaction potentials

A working model of baryon masses is presented, based on relativistic kinematics of three quarks sharing a common characteristic momentum. The system mass is defined as the sum of relativistic energies of the components without invoking gluon fields. The sole calibration parameter—the momentum scale $p_0$—is fixed once using the proton mass. The model reproduces the proton mass with 0.003\% accuracy, the neutron with 0.14\% accuracy, and $\Delta$-resonances with 1.5\% accuracy. For strange baryons, deviations range from 5--15\%, indicating the limits of the ultra-relativistic approximation and the necessity of accounting for color structure as a geometric property of projection from Level A. The hadron radius is not used to calculate mass—it emerges as a consequence of dynamics. This work is under development; the purpose of publication is to attract constructive criticism and demonstrate the viability of the conceptual approach. The model is available under CC BY 4.0 license: \url{https://doi.org/10.5281/zenodo.18518434}.