Multi-Horn Geometric Dynamics: A Coupled Rotation and Singular-Junction Framework

This working paper introduces the Multi-Horn Geometric Dynamics framework, an idealized mathematical model consisting of independently rotating horn-torus components connected through a shared singular junction. The framework combines differential geometry, complex rotational symmetry, Hamiltonian mechanics, and operator theory to investigate geometric focusing, coupled phase dynamics, and wave propagation across singular structures. A coupled Hamiltonian formulation yields conservation of total angular momentum and an analytically reducible two-component phase model. The corresponding small-amplitude resonance frequency is derived under explicitly stated assumptions. The paper also examines the singular behavior of the horn geometry, the role of self-adjoint boundary conditions, and the use of quantum graphs as simplified spectral models. The proposed framework is intended as a mathematical research model rather than an established physical theory. Its relationship to physical spacetime, gravitational phenomena, and quantum measurement remains conjectural and requires further theoretical and empirical investigation. Document status: Research Note, Version 0.2.1 (October 2026). Not peer-reviewed.