Paper 34: Hamiltonian Dynamics of Angular Coherence in the Holosphere Lattice

This paper develops a Hamiltonian framework for Holosphere Theory, a model in which the universe is composed of discrete, rotating Holospheres—each formed from nested Planckscale spheres. Physical behavior arises not from point particles or continuous fields, but from the propagation of angular coherence across a cuboctahedral lattice. We formulate a discrete Hamiltonian system in which the angular phase θi and the associated coherence strain momentum pi act as canonical variables. [6] The resulting equations of motion describe defect propagation, orbital quantization, spinor dynamics, and gravitational-like effects as outcomes of tension between phase-aligned Holospheres. By deriving the Hamiltonian from a previously established Lagrangian action principle, we unify the discrete dynamical laws of the Holosphere lattice under a single variational framework. This coherence-based Hamiltonian reproduces classical, quantum, and relativistic behavior as limiting cases of angular strain propagation, and lays the foundation for path integral and field-theoretic extensions in future work.