Classical Stability and Poincaré Orbit of a Localized Charged Cell in the Axis Model: Energy-Space Hamiltonian Stability and an Exact Lorentz Mass Hyperboloid

This release presents the classical stability and Poincaré-orbit analysis of the localized charged cell constructed in the Axis Parent. The paper establishes linear Hamiltonian stability of the charged-cell solution after the physical charge and momentum constraints are imposed and the phase and translational zero modes are removed. On the resulting positive energy space, the reduced evolution is unitary and the fluctuation spectrum is confined to the imaginary axis, providing a controlled classical stability certificate for the localized cell. Lorentz covariance then generates the complete family of uniformly moving solutions. These solutions form an exact classical relativistic mass orbit, with a certified energy range that remains below the free charged-field threshold. Together with the Parent localization theorem, the result establishes a localized, finite-energy charged classical object with controlled linear stability and relativistic propagation. The associated release contains the manuscript, source, figures, computational authority packages, executable tests, claim and holdout records, and reproducibility metadata. The work provides the classical one-cell foundation for subsequent quantum, multi-cell, spin/statistics, and particle-representation constructions in the Axis Model.